CHECK YOUR GRASP. 5. Work done in time t on a body of mass m which is accelerated from rest to a speed v in time t 1

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1 J-Physics XRCIS 1 CHCK YOUR GRSP SLCT TH CORRCT LTRNTIV (ONLY ON CORRCT NSWR) 1. person of 5 kg rests on a swing of length 1 aking an angle 37 O with the vertical. nother person pushes hi to swing on other side at 53 O with vertical. The work done by person is : [ g = 1 /s ] () 5 J () 9.8 J 1 J 1 J. The work done by the frictional force on a pencil in drawing a coplete circle of radius r = 1/ etre on the surface by a pencil of negligible ass with a noral pressing force N = 5 N (µ =.5) is : () + 4J () 3 J J 5J 3. rope is used to lower vertically a block of ass M by a distance x with a constant downward acceleration g/. The work done by the rope on the block is : () Mgx () 1 1 Mgx² Mgx Mgx² 4. The work done in oving a particle under the effect of a conservative force, fro position to is 3 joule and fro to C is 4 joule. The work done in oving the particle fro to C is : () 5 joule () 7 joule 1 joule 1 joule C 5. Work done in tie t on a body of ass which is accelerated fro rest to a speed v in tie t 1 as a function of tie t is given by : () 1 v t t 1 () v t t v t t t 1 v t 1 t 6. Velocity tie graph of a particle of ass kg oving in a straight line is as shown in figure. Work done by all the forces on the particle is : () 4 J () 4 J J J v (/s) t (s) 7. particle oves on a rough horizontal ground with soe initial velocity say v. If 3 of its kinetic energy is 4 node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 lost due to friction in tie t then coefficient of friction between the particle and the ground is : () v gt () v 4gt 8. block of ass oving with speed v copresses a spring through distance x before its speed is halved. What is the value of spring constant? () 3v 4x () v 4x 9. n engine can pull 4 coaches at a axiu speed of /s. Mass of the engine is twice the ass of every coach. ssuing resistive forces proportional to the weight, approxiate axiu speeds of the engine when it pulls 1 and 6 coaches are : () 8.5 /s and 15 /s respectively () 6.5 /s and 8 /s respectively 8.5 /s and 13 /s respectively 1.5 /s and 15 /s respectively 31 3v 4gt v x v gt v x

2 J-Physics 1 sall sphere starts falling fro a very large height and after falling a distance of 1 it attains the terinal velocity and continues to fall with this velocity. The work done by the atosphere during the first fall of 1 is : () Greater than the work done for next fall of 1 () Less than the work done for next fall of 1 qual to 1 g Greater than 1 g 1 1 force acts on a 3 g particle in such a way that the position of the particle as a function of tie is given by x= 3t 4t + t 3, where x is in eters and t is in seconds. The work done during the first 4 second is : () 384 J () 168 J 58 J 541 J 1. body is oved along a straight line by a achine delivering constant power. The distance oved by the body in tie t is proportional to : () t 1/ () t 3/4 t 3/ t 13. particle of ass is oving in a circular path of constant radius r such that its centripetal acceleration a C is varying with tie t as a C = k rt, where k is a constant. The power delivered to the particle by the force acting on it is : () k r () k r t 4 5 (k r t ) In the figure shown the potential energy (U) of a particle is plotted against its position 'x' fro origin. Then which of the following stateent is correct. particle at : () x 1 is in stable equilibriu () x is in stable equilibriu x 3 is in stable equilibriu None of these zero U O X 1 X X 3 X 1 5. The given plot shows the variation, the potential energy (U) of interaction between two particles with the separating distance (r) between the. Which of the above stateents are correct? (1) and D are equilibriu points () C is a point of stable equilibriu points (3) The force of interaction between the two particles is attractive between points C and D and repulsive between points D and on the curve. (4) The force of interaction between the particles is repulsive between points and F on the curve. () 1 and 3 () 1 and 4 and 4 and 3 U C D F r 16. weight is hung freely fro the end of a spring. boy then slowly pushes the weight upwards until the spring becoes slack. The gain in gravitational poetential energy of the weight during this process is equal to : () The work done by the boy against the gravitational force acting on the weight. () The loss of the stored energy by the spring inus the work done by the tension in the spring. The work done on the weight by the boy plus the stored energy lost by the spring. The work done on the weight by the boy inus the workdone by the tension in the spring plus the stored energy lost by the spring. 17. rope ladder with a length carrying a an of ass at its end is attached to the basket of balloon with a ass M. The entire syste is in equilibriu in the air. s the an clibs up the ladder into the balloon, the balloon descends by a height h. Then the potential energy of the an : () Increases by g ( h) () Increases by g Increases by gh Increases by g ( h) 3 node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

3 J-Physics 1 8. block attached to a spring, pulled by a constant horizontal force, is kept on a sooth surface as shown in the figure. Initially, the spring is in the natural state. Then the axiu positive work that the applied force F can do is : [Given that spring does not break] k F () F k () F k F k 1 9. siple pendulu has a string of length and bob of ass. When the bob is at its lowest position, it is given the iniu horizontal speed necessary for it to ove in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is : () 3g () 4g 5g 6g. In the previous question, when the string is horizontal, the net force on the bob is : () g () 3g 1g 4g 1. particle of ass is fixed to one end of a light rigid rod of length and rotated in a vertical circular path about its other end. The iniu speed of the particle at its highest point ust be : () zero () g 1.5g g. stone tied to a string of length L is whirled in a vertical circle, with the other end of the string at the centre. t a certain instant of tie, the stone is at its lowest position and has a speed u. The agnitude of the change in its velocity as it reaches a position where the string is horizontal is : () u gl () gl u gl (u gl ) 3. arble of ass and radius b is placed in a heispherical bowl of radius r. The iniu velocity to be given to the arble so that it reaches the highest point is : () g(r b) () g r g (r b ) g (r b ) 4. particle is placed at the top of a sphere of radius r. It is given a little jerk so that it just starts slipping down. Find the point where it leaves the sphere. () r/ () r/3 r/4 r 5. particle is oving in a circular path with a constant speed v. If is the angular displaceent, then starting fro =, the axiu and iniu change in the linear oentu will occur when value of is respectively : () 45º & 9º () 9º & 18º 18º & 36º 9º & 7º node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 6. In a siple pendulu, the breaking strength of the string is double the weight of the bob. The bob is released fro rest when the string is horizontal. The string breaks when it akes an angle with the vertical () cos () = 6 CHCK YOUR GRSP NSWR KY XRCIS 1 33 cos 3 1 = C D C D C C D C C D C D C C

4 J-Physics XRCIS RIN TSRS SLCT TH CORRCT LTRNTIVS (ON OR MOR THN ON CORRCT NSWRS) 1. In the figure shown, the syste is released fro rest. Find the velocity of block when block has fallen a distance 'l'. ssue all pulleys to be assless and frictionless. () g 5 5g None of these () g P. block of ass is attached to two spring of spring constant k 1 and k as shown in figure. The block is displaced by x towards right and released. The velocity of the block when it is at x/ will be : k 1 k () (k1 k )x () 3 (k1 k )x 4 (k1 k )x (k1 k )x 4 3. n object of ass slides down a hill of height h of arbitrary shape and after travelling a certain horizontal path stops because of friction. The friction coefficient is different for different segents for the entire path but is independent of the velocity and direction of otion. The work that a force ust perfor to return the object to its initial position along the sae path is : () gh () gh 4gh gh 4. bob hangs fro a rigid support by an inextensible string of length l. If it is displaced through a distance l (fro the lowest position) keeping the string straight & released, the speed of the bob at the lowest position is: () g () 3g g 5g 5. cube of ass M starts at rest fro point 1 at a height 4R, where R is the 1 radius of the circular track. The cube slides down the frictionless track and around the loop. The force which the track exerts on the cube at point is : () 3 g () g g cube will not reach the point. 6. Two bodies of ass 1 and ( > 1 ) are connected by a light inextensible string which passes through a sooth fixed pulley. The instantaneous power delivered by an external agent to pull 1 with constant velocity v is : () ( 1 ) g/v ( 1 ) gv 34 () ( 1 ) v/g ( 1 ) gv 1 4R F ext R node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

5 J-Physics 7. sall block slides with velocity.5 gr on the horizontal frictionless surface as shown in the figure. The block leaves the surface at point C. The angle in the figure is : v r C r g v C O D () cos 1 4 () cos 1 3 cos cos an places a chain of ass '' and length '' on a table slowly. Initially the lower end of the chain just touches the table. The an drops the chain when half of the chain is in vertical position. Then work done by the an in this process is : g 3g g () g () The potential energy of a particle of ass free to ove along x axis is given by U =½ kx for x < and U = for x (x denotes the x coordinate of the particle and k is a positive constant). If the total echanical energy of the particle is, then its speed at x = k is : () zero () 1. The blocks and shown in the figure have asses M = 5 kg and M = 4 kg. The syste is released fro rest. The speed of after has travelled a distance 1 along the incline is : () 3 g () 3 g 4 \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ 5 g g collar '' of ass kg is constrained to ove along a horizontal sooth and fixed circular track of radius 5. The spring lying in the plane of the circular track and having spring constant N/ is undefored when the collar is at ''. If the collar starts fro rest at ' the noral reaction exerted by the track on the collar when it passes through '' is : node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 7 () 36 N () 7 N 144 N 88 N 1. particle is projected along a horizontal field whose coefficient of friction varies as µ = where r is r the distance fro the origin in eters and is a positive constant. The initial distance of the particle is 1 fro the origin and its velocity is radially outwards. The iniu initial velocity at this point so that particle never stops is : () () g g 4 g 35 5 D C

6 J-Physics 1 3. Two identical blocks and are placed on two inclined planes as shown in diagra. Neglect air resistance and other friction. Choose the correct stateent : L N Fixed h h Fixed J K M O Stateent I: Kinetic energy of '' on sliding to J will be greater than the kinetic energy of on falling to M. Stateent II: cceleration of '' will be greater than acceleration of '' when both are released to slide on inclined plane. Stateent III : Work done by external agent to ove block slowly fro position to O is negative () stateent I is true () stateent II is true stateent I and III are true stateent II and III are true 1 4. Figure shows the roller coaster track. ach car will start fro rest at point and will roll with negligible friction. It is iportant that there should be at least soe sall positive noral force exerted by the track on the car at all points, otherwise the car would leave the track. With the above fact, the iniu safe value for the radius of curvature at point is (g = 1 /s ) : () () ////// / / ////// / //////////// /// particle '' of ass 1 7 kg is oving in the positive x direction. Its initial position is x = & initial velocity is 1 /s. The velocity at x = 1 is : (use the graph given) Power (in watts) 4 1 x (in ) () 4 /s () /s 3 / s 1/3 /s 1 6. fire hose has a diaeter of.5 c and is required to direct a jet of water to a height of at least 4. The iniu power of the pup needed for this hose is : () 1.5 kw () 4 kw 36.5 kw 48 kw 17. particle is projected vertically upwards with a speed of 16 /s, after soe tie, when it again passes through the point of projection, its speed is found to be 8 /s. It is known that the work done by air resistance is sae during upward and downward otion. Then the axiu height attained by the particle is : (Take g = 1 / s ) () 8 () force F 3i ˆ 4ˆj to final position d f 5i ˆ 4ˆj equal to : () 8 watt N acts on a kg ovable object that oves fro an initial position d i 3i ˆ ˆj () in 6s. The average power delivered by the force during the interval is 5 6 watt 15 watt 5 3 watt 36 node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

7 J-Physics 1 9. wedge of ass M fitted with a spring of stiffness 'k' is kept on a sooth horizontal surface. rod of ass is kept on the wedge as shown in the figure. Syste is in equilibriu. ssuing k that all surfaces are sooth, the potential energy stored in the spring is: M ( () g tan k () g tan k g tan k g tan k. In the figure, a block slides along a track fro one level to a higher level, by oving through an interediate valley. The track is frictionless untill the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed v is 6 /s, the height difference h is 1.1 and the coefficient of kinetic friction µ is.6. The value of d is v µ=.6 h µ = () 1.17 () ball rolls down an inclined plane figure. The ball is first released fro rest fro P and then later fro Q. Which of the following stateent is/are correct? () The ball takes twice as uch tie to roll fro Q to O as it does to Q roll fro P to O. () The acceleration of the ball at Q is twice as large as the acceleration at P. P h The ball has twice as uch K.. at O when rolling fro Q as it does when h rolling fro P O None of the above. car of ass starts oving so that its velocity varies according to the law v a s, where a is a constant, and s is the distance covered. The total work perfored by all the forces which are acting on the car during the first t seconds after the beginning of otion is : () a 4 t /8 () a t 4 /8 a 4 t /4 a t 4 /4 node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 3. block of ass is attached with a assless spring of force constant k. The block is placed over a rough inclined surface for which the coefficient of friction is = 3/4. The iniu value of M required to ove the block up the plane is : (Neglect ass of string and pulley and friction in pulley) () 3 5 () bob is suspended fro a crane by a cable of length = 5. The crane and load are oving at a constant speed v. The crane is stopped by a buper and the bob on the cable swings out an angle of 6. The initial speed v is (g = 9.8 /s ) () 1 /s () 7 /s 4 /s /s 37 v 37 M

8 J-Physics 5. If one of the forces acting on a particle is conservative then : () Its work is zero when the particle oves exactly once around any closed path. () Its work equals the change in the kinetic energy of the particle. It obeys Newton's second law. Its work depends on the end points of the otion, not on the path between. 6. particle of ass = 1 kg lying on x axis experiences a force given by law F=x(3x ) Newton, where x is the x coordinate of the particle in eters. The points on x axis where the particle is in equilibriu are : () x = () x = 1/3 x = /3 x = 1 7. With what iniu velocity v should block be projected fro left end towards end such that it reaches the other end of conveyer belt oving with constant velocity v? Friction coefficient between block and belt is. v v () gl () gl 3 gl gl 8. light spring of length c and force constant N/c is placed vertically on a table. sall block of ass 1 kg falls on it. The length h fro the surface of the table at which the block will have the axiu velocity is : () c () 15 c 1 c 5c 9. In the figure shown all the surfaces are frictionless, and ass of the block, = 1 kg. The block and wedge are held initially at rest. Now wedge is given a horizontal acceleration of 1 /s by applying a force on the wedge, so that the block does not slip on the wedge. Then work done by the noral force in ground frae on the block in 3 seconds is : M 1/s () 3J () 6 J 15 J 1 3 J 3. When a conservative force does positive work on a body : () The potential energy increases () The potential energy decreases Total energy increases Total energy decreases kg block collides with a horizontal weightless spring of force constant.75 N 1. The block copresses the spring 4. fro the rest position. If the coefficient of kinetic friction between the block and horizontal surface is.5, the speed of the block at the instant of collision is : ().4 s 1 () 4 s 1.8 s 1 8 s 1 3. cceleration versus tie graph of a particle oving in a straight line is as a shown in adjoining figure. If initially particle was at rest then corresponding kinetic energy versus tie graph will be: () K t () K t 38 K t (/s ) K t t(s) node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

9 3 3. particle is oved fro (, ) to (a, a) under a force F (3i ˆ 4ˆj) fro two paths. Path 1 is OP and path is OQP. Let W 1 and W be the work done by this force in these two paths. Then : () W 1 = W () W 1 = W W = W 1 W = 4W 1 y O 45 J-Physics 3 4. particle of ass begins to slide down a fixed sooth sphere fro the top. What is the tangential acceleration when it breaks off the sphere? () g 3 () 5g 3 g g achine, in an auseent park, consists of a cage of the end of one ar, hinged at O. The cage revolves along a vertical circle of radius r (CDFGH) about its hinge O, at constant linear speed v= gr. The cage is so attached that the an of weight 'W' standing on a weighing achine, inside the cage, is always vertical. Then which of the following is correct () The weight reading at is greater than the weight reading at by W () The weight reading at G = W The ratio of the weight reading at to that at = The ratio of the weight reading at to that at C = G F H P(a, a) Q O x D C 3 6. hollow vertical cylinder of radius r and height h has a sooth internal surface. sall particle is placed in contact with the inner side of the upper ri, at point, and given a horizontal speed u, tangential to the ri. It leaves the lower ri at point, vertically below. If n is an integer then () u h n r g () h n r r n u n h gh u h 3 7. The kinetic energy K of a particle oving along a circle of radius R depends upon the distance s, as K = as². The force acting on the particle is node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 () s² a R () s² as 1 R 1 39 as a 3 8. siple pendulu of length L and ass (bob) M is oscillating in a plane about a vertical line between angular liits and. For an angular displaceent, [ <] the tension in the string and velocity of the bob are T and v respectively. The following relations hold good under the above conditions () T cos Mg Tangential acceleration = g sin () Mv T Mg cos L T=Mg cos RIN TSRS NSWR KY XRCIS Q u e n s. C C C C C D Q u e n s. C C,C,D,C C Q u e n s. D,,C,D,C

10 J-Physics XRCIS 3 MISCLLNOUS TYP QUSTIONS TRU FL S 1. Mechanical energy of a body cannot be negative.. Net work done by external forces on a oving body is sae as observed fro different inertial fraes. 3. Work done by a non-conservative force is always negative. 4. Work done by all internal conservative forces is required to change in its potential energy. FILL IN TH LNKS 1. The work done in holding a 15 kg suitcase while waiting for a bus for 15 inute is.... body of ass M tied to a string is lowered at a constant acceleration of (g/4) through a vertical distance h. The work done by the string will be n open knife edge of ass M is dropped fro a height h on a wooden floor. If the blade penetrates 's' into the wood, the average resistance offered by the wood to the blade is The power of a pup which raises 1 kg of a water in 1 s to a height 1 is... kw. 5. ball suspended by a thread swings in a vertical plane so that its acceleration values in the extree and lowest position are equal. The thread deflection angle in the extree position is. M TCH TH COLUMN 1. block of ass is stationary with respect to a rough wedge as shown in figure. Starting fro rest, in tie t work done on the block : ( = 1kg, = 3, a = /s, t = 4s) a Colun I Colun II () y gravity (p) 144 J () y noral reaction (q) 3 J y friction (r) 56 J y all the forces (s) 48 J (t) None. cceleration 'a' versus x and potential energy 'U' versus x graph of a particle oving along x axis is as shown in figure. Mass of the particle is 1kg and velocity at x = is 4 /s. t x = 8 : a(/s ) x() Colun I Colun II () Kinetic energy (p) 1J () Work done by conservative forces (q) 4 J Total work done (r) 18 J Work done by external forces (s) 11 J 4-1 U(J) 4 8 x() (t) 1 J node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

11 J-Physics 3. block of ass lies on wedge of ass M. The wedge in turn lies on sooth horizontal surface. Friction is absent everywhere. The wedge block syste is released fro rest. ll situation given in colun I are to be estiated in duration the block undergoes a vertical displaceent 'h' starting fro rest (assue the block to be still on the wedge, g is acceleration due to gravity). M Colun I Colun II () Work done by noral reaction acting on the block is (p) Positive () Work done by noral reaction (q) Negative (exerted by block) acting on wedge is The su of work done by noral reaction (r) Zero on block and work done by noral reaction (exerted by block) on wedge is Net work done by all forces on block is (s) Less than gh in agnitude 4. In vertical circular otion of a bob, atch the entries of colun I with entries of colun II. Here v is the velocity of bob at lowest point & T is tension in string. Colun I (Speed at lowest point) Colun II (Possi ble si tuation) () v = 5g (p) T lowest T highest = 6g () v = g (q) String will slack for a finite tie v = g (r) bob will oscillate v = 3 g (s) bob will coplete the circle SSRTION RSON 1. Stateent 1 : The work done in pushing a block is ore than the work done in pulling the block in a rough surface. a n d Stateent : In the pushing condition ore noral reaction increases the frictional force. () Stateent I is true, Stateent II is true ; Stateent II is correct explanation for Stateent I. () Stateent I is true, Stateent II is true ; Stateent II is NOT a correct explanation for stateent I Stateent I is true, Stateent II is false Stateent I is false, Stateent II is true node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65. Stateent 1 : One end of ideal assless spring is connected to fixed vertical wall and other end to a block of ass initially at rest on sooth horizontal surface. The spring is initially in natural length. Now a horizontal force F acts on block as shown. Then the axiu extension in spring is equal to axiu copression in spring. a n d Stateent : To copress or to expand an ideal unstretched spring by equal aount, sae work is to done on spring. () Stateent I is true, Stateent II is true ; Stateent II is correct explanation for Stateent I. () Stateent I is true, Stateent II is true ; Stateent II is NOT a correct explanation for stateent I Stateent I is true, Stateent II is false Stateent I is false, Stateent II is true 41 F

12 J-Physics 3. Stateent 1 : The work done by friction is always negative. a n d Stateent : If frictional force acts on a body its kinetic energy ay decrease. () Stateent I is true, Stateent II is true ; Stateent II is correct explanation for Stateent I. () Stateent I is true, Stateent II is true ; Stateent II is NOT a correct explanation for stateent I Stateent I is true, Stateent II is false Stateent I is false, Stateent II is true 4. Stateent 1 : particle is rotated in a vertical circle with the help of a string. Power produced by tension in the string on the particle is zero. a n d S t a t e e n t : Tension is always perpendicular to instantaneous velocity. () Stateent I is true, Stateent II is true ; Stateent II is correct explanation for Stateent I. () Stateent I is true, Stateent II is true ; Stateent II is NOT a correct explanation for stateent I Stateent I is true, Stateent II is false Stateent I is false, Stateent II is true 5. State ent 1 : body can have energy without having oentu. a n d State ent : body can have oentu without having echanical energy. () Stateent I is true, Stateent II is true ; Stateent II is correct explanation for Stateent I. () Stateent I is true, Stateent II is true ; Stateent II is NOT a correct explanation for stateent I Stateent I is true, Stateent II is false Stateent I is false, Stateent II is true 6. State ent 1 : If the internal forces are conservative, the work done by the external force is equal to the change in echanical energy. a n d State ent : Work done on a syste by all the (external and internal) force is equal to the change in its kinetic energy and the change in the potential energy of a syste corresponding to conservative internal forces is equal to negative of the work done by these forces. () Stateent I is true, Stateent II is true ; Stateent II is correct explanation for Stateent I. () Stateent I is true, Stateent II is true ; Stateent II is NOT a correct explanation for stateent I Stateent I is true, Stateent II is false Stateent I is false, Stateent II is true 7. State ent 1 : When a gas is allowed to expand, work done by gas is positive. a n d State ent : In expansion of a gas the force due to gaseous pressure and displaceent (of piston) are in the sae direction. () Stateent I is true, Stateent II is true ; Stateent II is correct explanation for Stateent I. () Stateent I is true, Stateent II is true ; Stateent II is NOT a correct explanation for stateent I Stateent I is true, Stateent II is false Stateent I is false, Stateent II is true 8. State ent 1 : body at rest ay be in equilibriu. a n d State ent : body in equilibriu is at rest. () Stateent I is true, Stateent II is true ; Stateent II is correct explanation for Stateent I. () Stateent I is true, Stateent II is true ; Stateent II is NOT a correct explanation for stateent I Stateent I is true, Stateent II is false Stateent I is false, Stateent II is true 4 node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

13 COMPRHNSION QUSTIONS J-Physics Coprehension # 1 block of ass is kept in an elevator which starts oving downward with an acceleration a as shown in figure. The block is observed by two observers and for a tie interval t. a 1. The observer finds that the work done by gravity is () 1 g t () 1 g t 1 gat 1 gat. The observer finds that work done by noral reaction N is () zero () Nat + Nat None of these 3. The observer finds that work done by pseudo force is () zero () a t + a t gat 4. ccording to observer, the net work done on the block is () 1 a t () 1 a t 1 gat 1 gat 5 ccording to the observer () the work done by gravity is zero the work done by pseudo force is zero () the work done by noral reaction is zero all the above Coprehension # node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 Two identical beads are attached to free ends of two identical springs of spring constant 43 ( 3 )g k. Initially both 3 R springs ake an angle of 6 at the fixed point N. Noral length of each spring is R. Where R is the radius of sooth ring over which bead is sliding. Ring is placed on vertical plane and beads are at syetry with respect to vertical line as diaeter. 1. Noral reaction on one of the bead at initial oent due to ring is N () g/ () 3 g/ g Insufficient data

14 J-Physics. Relative acceleration between two beads at the initial oent () g/ vertically away fro each other () g/ horizontally towards each other g/ 3 vertically away fro each other g/ 3 horizontally towards each other 3. The speed of bead when spring is at noral length () 3 gr 3 () 3 gr 3 gr 3 3gR 4. Choose the correct stateent () Maxiu angle ade by spring after collision is sae as that of initial oent () If the collision is perfectly inelastic, the total energy is conserved If the collision is perfectly elastic, each bead undergoes SHM oth Linear oentu and angular oentu with respect to centre of sooth ring are conserved only at the instant of collision. Coprehension # 3 The bob of siple pendulu of length is released fro a point in the sae horizontal line as the point of suspension (O) and at a distance fro it. o N 1. The velocity of the bob at the lowest point of the string will be () v g () v g v 3g v g. If the string is catched by a nail located vertically below the point of suspension and the bob just swings around a coplete circle around the nail, then the distance of the nail fro point of suspension. () (/5) () (/3) (3/5) (1/3) 3. If the string of the pendulu is ade of rubber then how uch will it be stretched on reaching the bob at the lowest point. () g/k () 3g/k 5 g/k g/k Coprehension # 4 ball is released fro point as shown in figure. The ball leaves the track at. ll surfaces are sooth Let h be the axiu height fro ground reached by ball after leaving track at. Then : () h = 6 () h < 6 h > 6 speed of ball at will change if shape of track is changed keeping h and h constant. If track akes an angle 3 with horizontal at then axiu height attained by ball will be : () 3 () node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

15 Coprehension # 5 In the figure shown upper block is given a velocity of 6 /s and the is stopped. Rough 1kg kg Sooth 6/s J-Physics lower block 3 /s. When relative otion between 1. () Work done by friction on upper block is negative () Work done by friction on both the blocks is positive Work done by friction on lower block is negative Work done by friction on both the blocks is negative. () Work done by friction on upper block is 1 J () Work done by friction on lower block is + 1 J Net work done by friction is zero ll of the above Coprehension # 6 In a conservative force field we can find the radial coponent of force fro the potential energy function by using F = du. Here, a positive force eans repulsion and a negative force eans attraction. Fro the given potential dr energy function U(r) we can find the equilibriu position where force is zero. We can also find the ionisation energy which is the work done to ove the particle fro a certain position to infinity. Let us consider a case in which a particle is bound to a certain point at a distance r fro the centre of the force. The potential energy of the particle is : U(r) = r are positive constants. r 3/s where r is the distance fro the centre of the force and and 1. The equilibriu distance is given by : () () 3. The equilibriu is : () Stable () Unstable Neutral Cannot be predicted 3. The work required to ove the particle fro equilibriu distance to infinity is : () 4 () If the total energy of the particle is =, and it is known that the otion is radial only then the velocity 16 is zero at : (here, r = equilibriu distance) node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 () r 3 Coprehension # 7 () r 3 Ra and Shya are two fast friends since childhood. Shya neglected studies and now has no eans to earn oney other than a cael whereas Ra becoes an engineer. Now both are working in the sae factory. Shya uses cael to transport the load within the factory. 45 r r 5

16 J-Physics Due to low salary & degradation in health of cael, Shya becoes worried and eet his friend Ra and discusses his proble. Ra collected soe data & with soe assuptions concluded the following: The load used in each trip is 1 kg and has friction coefficient µ k =.1 and µ s =.. Mass of cael is 5 kg. Load is accelerated for first 5 with constant acceleration, then it is pulled at a constant speed of 5/s for k and at last stopped with constant retardation in 5. Fro biological data, the rate of consuption of energy of cael can be expressed as P = v+ 1 4 J/s where P is the power and v is the velocity of the cael. fter calculations on different issues Ra suggested proper food, speed of cael etc. to his friend. For the welfare of Shya, Ra wrote a letter to the anageent to increase his salary. (ssuing that the cael exerts a horizontal force on the load) : 1. Sign of work done by the cael on the load during parts of otion : accelerated otion, unifor otion and retarted otion respectively are : () +ve, +ve, +ve () +ve, +ve, ve +ve, zero, ve +ve, zero, +ve. The ratio of agnitude of work done by cael on the load during accelerated otion to retarded otion is () 3 : 5 (). : 1 1 : 1 5 : 3 3. Maxiu power transitted by the cael to load is () 65 J/s () 5 J/s 1 5 J/s 15 J/s 4. The ratio of the energy consued of the cael during unifor otion for the two cases when it oves with speed 5 /s to the case when it oves with 1 /s. () 19 () The total energy consued of the cael during the trip of 1 is () J () J. 1 4 J J Coprehension # 8 block of ass oving with a velocity v on a sooth horizontal surface strikes and copresses a spring of stiffness k till ass coes to rest as shown in the figure. This phenoenon is observed by two observers : : Standing on the horizontal surface; : Standing on the block 1. To an observer, the work done by spring force is () negative but nothing can be said about its agnitude () positive but nothing can be said about its agnitude + v 46 k 1 v 1 v node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

17 J-Physics. To an observer, the work done by the noral reaction N between the block and the spring on the block is () zero () 1 v + 1 v None of these 3. To an observing, the net work done on the block is () v () + v 1 v zero 4. ccording to the observer () the kinetic energy of the block is converted into the potential energy of the spring () the echanical energy of the spring ass syste is conserved the block loses its kinetic energy because of the negative work done by the conservative force of spring all the above 5. To an observer, when the block is copressing the spring () velocity of the block is decreasing () retardation of the block is increasing kinetic energy of the block is zero all the above 6. ccording to observer, the potential energy of the spring increases () due to the positive work done by pseudo force () due to the negative work done by pseudo force due to the decrease in the kinetic energy of the block all the above Coprehension # 9 sall sphere of ass suspended by a thread is first taken aside so that the thread fors the right angle with the vertical and then released, then 1. The total acceleration of the sphere and the thread tension as function of, the angle of deflection of the thread fro the vertical will be () g 1 3 cos, T = 3 g cos () gcos, T = 3g cos node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 g 1 3 sin, T = 5g cos gsin, T = 5 g cos. The thread tension at the oent when the vertical coponent of the sphere's velocity is axiu will be () g () g g 3 g 3 3. The angle between the thread and the vertical at the oent when the total acceleration vector of the sphere is directed horizontally will be () cos = 1 3 () 1 cos 3 47 sin 1 3 sin 1

18 J-Physics Coprehension # 1 vertical frictionless seicircular track of radius R is fixed on the edge of ovable trolley. Initially the syste is at rest and a ass is kept at the top of the track. The trolley starts oving to the right with a unifor horizontal acceleration a = g 9. The ass slides down the track, eventually losing contact with it and dropping to the floor h below the trolley. R h= 4R 3 a= g 9 1. The angle with vertical, at which it losses contact with the trolley is () 37 () 53 cos 1. The height at which ass losing contact is () R () R R R 3. The tie taken by the ass to drop on the floor, after losing contact is 1 cos 3 () R 3g () R g R 3g Can't be deterined MISCLLNOUS TYP QUSTION NSWR KY XRCIS 3 Tr ue / False 1. F. F 3. F 4. T Fill in the lanks 1. zero. g Mgh 3. h s 3 4 s sin 1 5 or tan 1 Match the Colun 1. () t, () p, s, q. () r, () q, p, t 3. () q, s () p,s r,s p,s 4. () p,s () r, q, p,s ssertion Reason 1.. D 3. D C Coprehension ased Questions Coprehension #1 : 1. C. D D Coprehension # : 1. C. D 3. C 4. D Coprehension #3: 1.. C 3. Coprehension #4 : 1.. Coprehension #5 : 1.. Coprehension #6 : C 4. Coprehension #7 : 1.. D D 5. Coprehension #8 : C 4. D 5. C 6. Coprehension #9 : 1.. C 3. Coprehension #1 : 1.. D node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

19 J-Physics XRCIS 4 () CONCPTUL SUJCTIV XRCIS 1. In the figure () and () C, DG and GF are fixed inclined planes, C = F = x and = D = y. sall block of ass M is released fro the point. It slides down C and reaches C with a speed v C. The sae block is released fro rest fro the point D. It slides down DGF and reaches the point F with speed v F. The coefficients of kinetic friction between the block and both the surfaces C and DGF are µ. Calculate v C and v F. D G (a) C (b) F. body of ass kg is being dragged with a unifor velocity of /s on a rough horizontal plane. The coefficient of friction between the body and the surface is., J = 4. J/cal and g = 9.8 /s. Calculate the aount of heat generated in 5 s. 3. Two blocks and are connected to each other by a string and a spring; the string pass overs a frictionless pulley as shown in the figure. lock slides over the horizontal top surface of a stationary block C and the block slides along the vertical side of C, both with the sae unifor speed. The coefficient of friction between the surface and the block is.. Force constant of the spring is 196 N/. If ass of block is kg, calculate the ass of block and the energy stored in the spring. C 4. particle is oving in x direction, under the influence of force F = sinx. Find the work done by another external agent in slowly oving a particle fro x= to x =.5. node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 5. particle of ass 5 kg is free to slide on a sooth ring of radius r= c fixed in a vertical plane. The particle is attached to one end of a spring whose other end is fixed to the top point O of the ring. Initially the particle is at rest at a point of the ring such that OC = 6, C being the centre of the ring. The natural length of the spring is also equal to r = c. fter the particle is released and slides down the ring the contact force between the particle & the ring becoes zero when it reaches the lowest position. Deterine the force constant of the spring. O C 6. particle of ass oves along a circle of radius R with a noral acceleration varying with tie as a bt, 6 where b is a constant. Find the tie dependence of the power developed by all the forces acting on the particle, and the ean value of this power averaged over the first t seconds after the beginning of otion. 49 n

20 J-Physics 7. light string CD whose id point is C passes through sooth rings and D, which are fixed in a horizontal plane distance a apart. To each of the points, C and is attached a ass. Initially C is held at rest at O (id point D) and is then set free. What is the distance OC when C coes to instantaneous rest? a C D \\\\\\\\\ \\\\\\\\\ 8. The potential energy of a particle of ass 1kg free to ove along x-axis is given by V(x) = If total echanical energy of the particle is J, then find the axiu speed of the particle. 9. For what iniu value of 1 the block of ass will just leave the contact with surface? F HG I x x joule. KJ K 1 1. particle of ass 3 kg is rotating in a circle of radius 1 such that the angle rotated by its radius is given by =3 (t + sint). Find the net force acting on the particle when t = / The bob of a siple pendulu of length is released fro point P.What is the angle ade by the direction of net acceleration of the bob with the string at point Q. Q P h 1. ball of ass 1 kg is released fro position, inside a fixed wedge with a heispherical cut of radius.5 as shown in the figure. Find the force exerted by the vertical wall OM on wedge, when the ball is in position. (neglect friction everywhere). (Take g = 1 /s ) M O 6 C 5 N node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

21 J-Physics 1 3. For a particle rotating in a vertical circle with unifor speed, the axiu and iniu tension in the string are in the ratio 5:3. If the radius of vertical circle is, then find the speed of revolving body In the shown arrangeent a bob of ass '' is suspended by eans of a string connected to peg P. If the bob is given a horizontal velocity u having agnitude in subsequent otion. 3g, find the iniu speed of the bob P g 1 5. bead of ass is tied at one end of a spring of spring constant R and unstretched length R and other end to fixed point O. The sooth seicircular wire frae is fixed in vertical plane. Find the noral reaction between bead and wire just before it reaches the lowest point. u R k R/ O 1 6. sall block of ass is projected horizontally fro the top of the sooth heisphere of radius r with speed u as shown. For values of u u, it does not slide on the heisphere (i.e. leaves the surface at the top itself). r u node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 CONCPTUL SUJCTIV XRCIS NSWR KY X RCIS 4 ( ) 1. v C = v F = gy gx. 9.5 cal 3. 1 kg,.98 J 4. 1J 5. 5 N/ 6. Rbt, Rbt 9. 1 = (i) For u = u, it lands at point P on the ground Find OP. (ii) For u=u /3, find the height fro the ground at which it leaves the heisphere. (iii) Find its net acceleration at the instant it leaves the heisphere s a N 11. tan 1 g O sin h 8. 5 s g 16. (i) r, (ii) h= 19r 7 (iii) g N

22 J-Physics XRCIS 4 () RIN STORMING SUJCTIV XRCIS 1. particle of ass is hanging with the help of an elastic string of unstretched length a and force constant g a. The other end is fixed to a peg on vertical wall. String is given an additional extension of a in vertical downward direction by pulling the ass and released fro rest. Find the axiu height reached by it during its subsequent otion above point of release. (Neglect interaction with peg if any)..5 kg block slides fro the point (see figure) on a horizontal track with an initial speed of 3 /s towards a weightless horizontal spring of length 1 and force constant N/. The part of the track is frictionless and the part C has the coefficients of static and kinetic friction as. and. respectively. D C If the distance and D are and.14 respectively, find the total distance through which the block oves before it coes to rest copletely. (Take g = 1 /s ). 3. body of ass kg is oving under the influence of a central force whose potential energy is given by U(r) = r 3 J. If the body is oving in a circular orbit of radius 5, then find its energy. 4. square plate is firly attached to a frictionless horizontal plane. D a One end of a taut cord is attached to point of the plate and the a other end is attached to a sphere of ass. In the process, the cord gets wrapped around the plate. The sphere is given an initial 4a velocity v on the horizontal plane perpendicular to the cord which causes it to ake a coplete circle of the plate and return to point. Find the velocity of the sphere when it hits point again after 9 oving in a circle on the horizontal plane. lso find the tie taken v by the sphere to coplete the circle. C 5. sall bead of ass is free to slide on a fixed sooth vertical wire, as indicated in the diagra. One end of a light elastic string, of unstretched length a and force constant g/a is attached to. The string passes through a sooth fixed ring R and the other end of the string is attached to the fixed point, R being horizontal. The point O on the wire is at sae horizontal level as R, and R = RO =a. (i) In the equilibriu position, find O. (ii) The bead is raised to a point C of the wire above O, where OC =a, and is released fro rest. Find the speed of the bead as it passes O, and find the greatest depth below O of the bead in the subsequent otion. O a R a 6. ring of ass slides on a sooth vertical rod. light string is attached to the ring and is passing over a sooth peg distant a fro the rod, and at the other end of the string is a ass M (M>). The ring is held on a level with the peg and released. Show that Ma it first coes to rest after falling a distance M 7. string, with one end fixed on a rigid wall, passing over a fixed frictionless pulley at a distance of fro the wall, has a point ass M = kg attached to it at a distance of 1 fro the wall. ass =.5 kg attached at the free end is held at rest so that the string is horizontal between the wall and the pulley and vertical beyond the pulley. What will be the speed with which the ass M will hit the wall when the ass is released? 5 = M a M node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

23 J-Physics 8. In figure two identical springs, each with a relaxed length of 5 c and a spring constant of 5 N/, are connected by a short cord of length 1 c. The upper string is attached to the ceiling, a box that weighs 1N hangs fro the lower spring. Two additional cords, each 85 c long, are also tied to the assebly; they are lip (i.e. slack). (i) If the short cord is cut, so that the box then hangs fro the springs and the two longer cords, does the box ove up or down? (ii) How far does the box ove before coing to rest again? 9. '' block of ass is held at rest on a sooth horizontal floor. light frictionless, sall pulley is fixed at a height of 6 fro the floor. light inextensible string of length 16, connected with passes over the pulley and another identical block is hung fro the string. Initial height of is 5 fro the floor as shown in figure. When the syste is released fro rest, starts to ove vertically downwards and slides on the floor towards right. (i) If at an instant string akes an angle with horizontal, calculate relation between velocity u of and v of (ii) Calculate v when strikes the floor particle is suspended vertically fro a point O by an inextensible O L/8 assless string of length L. vertical line is at a distance L 8 fro O as shown in figure. The object is given a horizontal velocity u. t soe point, its otion ceases to be circular and eventually the object passes through the line. t the instant of crossing, its velocity is horizontal. Find u. L u 1 1. In the figure shown the pulley is sooth. The spring and the string are light. The block '' slides down fro the along the fixed rough wedge of inclination. ssuing that the block reaches the end of the wedge. Find the speed of the block at the end. Take the coefficient of friction between the block and the wedge to be µ and the spring k h W was relaxed when the blockwas released fro the top of the wedge. node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 1. s shown in the figure a person is pulling a ass '' fro ground on a fixed rough heispherical surface upto the top of the heisphere with the help of a light inextensible string. Find the work done by tension in the string if radius of heisphere is R and friction co efficient is µ. ssue that the block is pulled with negligible velocity. 53

24 J-Physics 1 3. Starting fro rest, a particle rotates in a circle of radius R = with an angular acceleration = 4 rad/sec. Calculate the agnitude of average velocity of the particle over the tie it rotates quarter circle stone weighing.5 kg tied to a rope of length.5 revolves along a circular path in a vertical plane. The tension of the rope at the botto point of the circle is 45 newtons. To what height will the stone rise if the rope breaks at oent the velocity is directed upwards? (g=1 /s ) RIN STORMING SUJCTIV XRCIS NSWR KY X R C I S 4 ( ) 1. 9a J 4. v=v, 5. (i) a (ii) ga, a s 1 8. up, c 9. u = v sec, v = 4 41 s 1 1. u = 3 3 gl v= 1. gr (1+ ) s a v 1 h gh k gh cot sin node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65

25 J-Physics XRCIS 5 [] PRVIOUS YR QUSTIONS 1. spring of force constant 8 N/ has an extension of 5 c. The work done in extending it fro 5 c to 15 c is- [ I - ] (1) 16 J () 8 J (3) 3 J (4) 4 J. spring of spring constant N/ is stretched initially by 5 c fro the unstretched position. Then the work required to stretch it further by another 5 c is- [ I - 3] (1) 1.5 N- () N- (3) 5. N- (4) 6.5 N- 3. body is oved along a straight line by a achine delivering a constant power. The distance oved by the body in tie t is proportional to- [ I - 3] (1) t 3/4 () t 3/ (3) t 1/4 (4) t 1/ 4. particle oves in a straight line with retardation proportional to its displaceent. Its loss of kinetic energy for any displaceent x is proportional to- [ I - 4] (1) x () e x (3) x (4) log e x 5. body of ass accelerates uniforly fro rest to v 1 in tie t 1. The instantaneous power delivered to the body as a function of tie t is- [I - 4] (1) v1t t1 () v t 1 t 1 (3) v1t t1 (4) v t 1 t1 6. unifor chain of length is kept on a table such that a length of 6 c hangs freely fro the edge of the table. The total ass of the chain is 4 kg. What is the work done in pulling the entire chain on the table [ I - 4] (1) 7. J () 3.6 J (3) 1 J (4) 1 J 7. bullet fired into a fixed target loses half of its velocity after penetrating 3c. How uch further it will penetrate before coing to rest, assuing that it faces constant resistance to otion? [ I - 5] (1) 3. c (). c (3) 1.5 c (4) 1. c 8. The block of ass M oving on the frictionless horizontal surface collides with the spring of spring constant k and copresses it by length L. The axiu oentu of the block after collision is- [ I - 5] M node6\_nod6 ()\Data\14\Kota\J-dvanced\SMP\Phy\Work Power nergy\ng\xercise.p65 (1) Mk L () kl M 55 (3) zero (4) 9. particle of ass 1 g is thrown vertically upwards with a speed of 5 /s. The work done by the force of gravity during the tie the particle goes up is- [ I - 6] (1).5 J () 1.5 J (3) 1.5 J (4).5 J 1. The potential energy of a 1 kg particle free to ove along the x-axis is given by V(x) = ML k 4 x x J. The total 4 echanical energy of the particle is J. Then, the axiu speed (in /s) is- [ I - 6] (1) 3/ () (3) 1/ (4)