Get Solution of These Packages & Learn by Video Tutorials on EXERCISE-1 CCELERATION

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1 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on EXECISE- SECTION : KINEMATICS OF CICULA CULA MOTION A. Figue shows a cicula path taken by a paticle. If the instantaneous velocity of the paticle is v = (m /s) î ( m/s) ĵ. Though which quadant is the paticle moving when it is tavelling (a) clockwise and (b) counte clockwise aound the cicle? SECTION (B) : ADIAL AND TANGENTIAL ACCELEA A CCELEATION B. A ca is moving with speed 0 m/sec on a cicula path of adius 500 m. Its speed is inceasing at the ate of m/sec. What is the acceleation of the ca at that moment? SECTION (C) : ADIUS OF CUVATUE AND DYNAMICS OF CICULA CULA MOTION C. A mass is kept on a hoizontal fictionless suface. It is attached to a sting and otates about a fixed cente at an angula velocity ω 0. If the length of the sting and angula velocity ae doubled, find the tension in the sting which was initially T 0. C. A simple pendulum oscillates in a vetical plane. When it passes though the mean position, the tension in the sting is times the weight of the pendulum bob. What is the maximum displacement of the pendulum of the sting with espect to the vetical. C. C 4. What is the adius of cuvatue of the paabola taced out by the pojectile in the pevious poblem in the pevious poblem at a point whee the paticle velocity makes an angle θ / with the hoizontal? A ceiling fan has a diamete (of the cicle though the oute edges of the thee blades) of 0 cm and pm 500 at full speed. Conside a paticle of mass g sticking at the oute end of a blade. How much focedoes it expeience when the fan uns at full speed? Who exets this foce on the paticle? How much foce does the paticle exet on the blade along its suface? SECTION (D) : CICULA CULA MOTION IN HOIZONTAL PLANE D. D. D. D 4. A sting beaks if its tension exceeds 0 newtons. A stone of mass 50 gm tied to this sting of length 0 cm is otated in a hoizontal cicle. Find the maximum angula velocity of otation. A body of mass m hangs at one end of a sting of length a, the othe end of which is fixed. It is given a hoizontal velocity u at its lowest position so that the sting would just become slack, when it makes an angle of 60 with the upwad dawn vetical line. Find the tension in the sting at point of pojection A ball is moving to and fo about the lowest point A of a smooth hemispheical bowl. If it is able to ise up to a height of 0 cm on eithe side of A, find its speed at A. (Take = 0 m/s, mass of the body 5 g). A motocyclist wants to dive on the vetical suface of wooden well of adius 5 m, with a minimum speed of 5 5 m/s. Find the minimum value of coefficient of fiction between the tyes and the wall of the well. (take g = 0 m/s ) Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 5 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

2 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on SECTION (E) : CICULA MOTION IN VETICAL PLANE E. E. E. A small body of mass m is allowed to slide on an inclined fictionless tack fom est position as shown in the figue. (i) Find the minimum height h, so that body may successfully complete the loop of adius. (ii) If h is double of that minimum height, find the esultant foce on the block at position H A nail is located at a cetain distance vetically below the point of suspension of a simple pendulum. The pendulum bob is eleased fom the position whee the sting makes an angle of 60 fom the vetical. Calculate the distance of the nail fom the point of suspension such that the bob will just pefom evolution with the nail as cente. Assume the length of pendulum to be m. A bucket tied at the end of a.6 m long sting is whiled in a vetical cicle with constant speed. What should be the minimum speed so that the wate fom the bucket does not spill, when the bucket is at the highest position (Take g = 0 m/sec ) SECTION (F) : MOTION OF A VEHICLE, CENTIFUGAL FOF OCE AND OTATION TION OF EATH F. F. F. F 4. F 5. F 6. A tain has to negotiate a cuve of adius 400 m. By how much height should the oute ail be aised with espect to inne ail fo a speed of 48 km/h? The distance between the ails is m : A paticle of mass m is constained to move along a goove which is being otated about a vetical axis though its cente with a constant angula velocity ω. If it stats at a distance fom the axis at t = 0, find its velocity elative to the goove when it is at a distance fom the cente A pak has a adius of 0m. If a vehicle goes ound it at an aveage speed of 8 km/h, what should be the pope angle of banking? If the oad of the pevious poblem is hoizontal (no banking), what should be the minimum fiction coefficient so that a scotte going at 8 km/h does not skid. A peson stands on a sping balance at the equato. By what faction is the balance eading less than his tue weight? (B) If the speed of eath s otation is inceased by such an amount that the balance eading is half the tue weight, what will be the length of the day in this case? A tun of adius 0 m is banked fo the vehicles going at a speed of 6 km/h. If the coefficient of static fiction between the oad and the tye is 0.4, what ae the possible speeds of a vehicle so that is neithe slips down no skids up? EXECISE- SECTION : KINEMATICS OF CICULA CULA MOTION A. The aveage acceleation vecto fo a paticle having a unifom cicula motion in one complete evolution: A constant vecto of magnitude v v (B) in magnitude and pependicula to the plane of cicle (C) Equal to the instantaneous acceleation vecto at the stat of the motion (D) A null vecto Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 6 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

3 Get Solution of These Packages & Lean by Video Tutoials on FEE Download Study Package fom website: & 0 A. A paticle moves along a cicle of adius m with constant tangential acceleation. It the velocity of the π paticle is 80 m/s at the end of the second evolution afte motion has begun, the tangential acceleation is: 60 π m/s (B) 40 π m/s (C) 40 m/s (D) 640 π m/s A. A 4. A 5. A 6. When a paticle moves in a cicle with a unifom speed its velocity and acceleation ae both constant (B) its velocity is constant but the acceleation changes (C) its acceleation is constant but the velocity changes (D) its velocity and acceleation both change An object follows a cuved path. The following quantities may emain constant duing the motion speed (B) velocity (C) acceleation (D) magnitude of acceleation Assume that the eath goes ound the sun in a cicula obit with a constant speed of 0 km/s. The aveage velocity of the eath fom st Jan, 90 to 0th June, 90 is zeo (B) The aveage acceleation duing the above peiod is 60 km/s. (C) The aveage speed fom st Jan, 90 to st Dec, 90 is zeo. (D) The instantaneous acceleation of the eath points towads the sun. The position vecto of a paticle in a cicula motion about the oigin sweeps out equal aea in equal time. Its velocity emains constant (B) speed emains constant (C) acceleation emains constant (D) tangential acceleation emains constant SECTION (B) : ADIAL AND TANGENTIAL ACCELEA A CCELEATION B. Two paticles P and Q ae located at distances P and Q espectively fom the cente of a otating disc such that P > Q : Both P and Q have the same acceleation (B) Both P and Q do not have any acceleation (C) P has geate acceleation than Q (D) Q has geate acceleation than P B. In unifom cicula motion, the quantity that emains constant is : linea velocity (B) centipetal foce (C) acceleation (D) speed B. When a paticle moves in a cicle with a unifom speed : Its velocity and acceleation ae both constant (B) Its velocity is constant but the acceleation changes (C) Its acceleation is constant but the velocity changes (D) Its velocity and acceleation both change B 4. Fo a paticle in a unifomly acceleated (speed inceasing unifomly) cicula motion : velocity is adial and acceleation is tangential only (B) velocity is tangential and acceleation is adial only (C) velocity is adial and acceleation has both adial and tangential components (D) velocity is tangential and acceleation has both adial and tangential components B 5. B 6. B 7. A moto cyclist going ound in a cicula tack at constant speed has constant linea velocity (B) constant acceleation (C) constant angula velocity (D) constant foce Fo a body in cicula motion with a constant angula velocity, the magnitude of the aveage acceleation ove a peiod of half a evolution is...times the magnitude of its instantaneous acceleation. π (B) π (C) π (D) A ca of mass m moves in a hoizontal cicula path of adius mete. At an instant its speed is v m/s and is inceasing at a ate a m/s, then the acceleation of the ca is : v a (B) a v + (C) v (D) a Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 7 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

4 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on B 8. B 9. The second s hand of a watch has length 6 cm. Speed of end point and magnitude of diffeence of velocities at two pependicula positions will be : 6.8 & 0 mm/s (B) 8.88 & 4.44 mm/s (C) 8.88 & 6.8 mm/s (D) 6.8 & 8.88 mm/s A paticle is going in a spial path as shown in figue with constant speed. The velocity of the paticle is constant (B) The acceleation of the paticle is constant (C) The magnitude of accleation is constant (D) The magnitude of accleation is deceasing continuously. SECTION (C) : ADIUS OF CUVATUE AND DYNAMICS OF CICULA CULA MOTION C. A paticle of mass m is executing unifom cicula motion on a path of adius. If p is the magnitude of its linea momentum. The adial foce acting on the paticle is : C. p m (B) m p (C) mp A tain is moving towads noth. At one place it tuns towads noth-east, hee we obseve that the adius of cuvatue of oute ail will be geate than that of the inne ail (B) the adius of the inne ail will be geate than that of the oute ail (C) the adius of cuvatue of one of the ails will be geate (D) The adius of cuvatue of the oute and inne ails will be the same SECTION (D) : CICULA CULA MOTION IN HOIZONTAL PLANE D. A stone of mass of 6 kg is attached to a sting 44 m long and is whiled in a hoizontal cicle. The maximum tension the sting can withstand is 6 newton. The maximum speed of evolution of the stone without beaking it, will be : 0 ms (B) 6 ms (C) 4 ms (D) ms D. D. D 4. D 5. Thee identical paticles ae joined togethe by a thead as shown in figue. All the thee paticles ae moving on a smooth hoizontal plane about point O. If the velocity of the outemost paticle is v 0, then the atio of tensions in the thee sections of the sting is : : 5 : 7 (B) : 4 : 5 (C) 7 : : 6 (D) : 5 : 6 A paticle is kept fixed on a tunatable otating unifomly. As seen fom the gound, the paticle goes in a cicle, its speed is 0 cm/s and acceleation is 0 cm/s.the paticle is now shifted to a new position to make the adius half of the oiginal value.the new values of the speed and acceleation will be 0 cm/s, 0 cm/s (B) 0 cm/s, 80 cm/s (C) 40 cm/s, 0 cm/s (D) 40 cm/s,40 cm/s A coin placed on a otating tuntable just slips if is placed at a distance of 4 cm fom the cente. if the angula velocity of the tuntable is doubled, it will just slip at a distance of cm (B) cm (C) 4 cm (D) 8 cm A od of length L is pivoted at one end and is otated with a unifom angula velocity in a hoizontal plane. Let T and T be the tensions at the points L/4 and L/4 away fom the pivoted ends. T > T (B) T > T (C) T = T (D) The elation between T and T depends on whethe the od otates clockwise o anticlockwise SECTION (E) : CICULA MOTION IN VETICAL PLANE E. When a paticle is otated in a vetical plane with constant angula velocity, magnitude of centipetal foce is : (D) p m Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 8 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

5 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on E. E. E 4. E 5. E 6. E 7. E 8. E 9. Maximum at highest point (B) Maximum at lowest point (C) Same at all points (D) zeo A motocycle is going on an ovebidge of adius. The dive maintains a constant speed. As the motocycle is ascending on the ovebidge, the nomal foce on it : incease (B) deceases (C) emains constant (D) fist inceases then deceases. A heavy paticle hanging vetically fom a point by a light inextensible sting of length l is stated so as to make a complete evolution in a vetical plane. The sum of the magnitude of tension at the ends of any diamete : fist incease then deceases (B) is constant (C) fist decease then inceases (D) deceases continuously In a cicus stuntman ides a motobike in a cicula tack of adius in the vetical plane. The minimum speed at highest point of tack will be : g (B) g (C) g (D) g A heavy mass is attached to a thin wie and is whiled in a vetical cicle. The wie is most likely to beak when the mass is at the highest point of the cicle (B) when the mass is at the lowest point of the cicle (C) when the wie is hoizontal (D) at an angle of cos (/) fom the upwad vetical A paticle is moving in a vetical cicle. The tensions in the sting when passing though two positions at angles 0 and 60 fom vetical (lowest positions) ae T and T espectively. Then T = T (B) T > T (C) T > T (D) Tension in the sting always emains the same A ca moves at a constant speed on a oad as shown in figue. The nomal foce by the oad on the ca in N A and N B when when it is at the points A and B espectively. N A = N B (B) N A > N B (C) N A < N B (D) insufficient Wate in a bucket is whiled in a vetical cicle with a sting attached to it.the wate does not fall down even when the bucket is inveted at the top of its path. We conclude that in this position. mg = mv (C) mg is not geate than mv (B) mg is geate than (D) mg is not less than A simple pendulum having a bob of mass m is suspended fom the ceiling of a ca used in a stunt film shotting. The ca moves up along an inclined cliff at a speed v and makes a jump to leave the cliff and lands at some distance. Let be the maximum height of the ca fom the top of the cliff. The tension is the sting when the ca is in ai is mv mg (B) mg (C) mg + mv mv mv (D) zeo SECTION (F) : MOTION OF A VEHICLE, CENTIFUGAL FOF OCE AND OTATION TION OF EATH F. The dive of a ca tavelling at speed suddenly sees a wall at a distance diectly in font of him. To avoid collision, he should apply bakes shaply (B) he should tun the ca shaply (C) he should apply bakes and then shaply tun (D) None of these Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 9 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

6 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on F. F. F 4. F 5. F 6. F 7. A cuved section of a oad is banked fo a speed v. If thee is no fiction between oad and tyes of the ca, then: ca is moe likely to slip at speeds highe than v than speeds lowe than v (B) ca cannot emain in static equilibium on the cuved section (C) ca will not slip when moving with speed v (D) none of the above A paticle of mass m is obseved fom an inetial fame of efeence and is found to move in a cicle of adius with a unifom speed v. The centifugal foce on it is (C) mv towads the cente (B) mv mv along the tangent though the paticle (D) zeo away fom the cente A tain A uns fom east to west and anothe tain B of the same mass uns fom west to east at the same speed along the equato. A pesses the tack with a foce F and B pesses the tack with a foce F. F > F (B) F < F (C) F = F (D) the infomation is insufficient to find the elation between F and F. A ca of mass M is moving hoizontaly on a cicula path of adius. At an instant its speed is v and is inceasing at a ate a. The acceleation of the ca is towads the cente of the path mv (B*) The magnitude of the fictional foce on the ca is geate than (C*) The fiction coefficient between the gound and the ca is not less than a/g. v (D) The fiction coefficient between the gound and the ca is µ = tan g A cicula oad of adius is banked fo a speed v = 40 km/h. A ca of mass attempts to go on the cicula oad. The fiction coefficient between the tye and the oad is negligible. The ca cannot make a tun without skidding. (B*) If the ca tuns at a speed less than 40 km/h, it will slip down mv (C) If the ca tuns at the cuent speed of 40 km/h, the foce by the oad on the ca is equal to (D*) If the ca tuns at the coect speed of 40 km/h, the foce by the oad on the ca is geate than mg as well as geate than mv A peson applies a constant foce F on a paticle of mass m and finds that the paticle moves in a cicle of adius with a unifom speed v as seen fom an inetial fame of efeence. This is not possible. (B) Thee ae othe foces on the paticle mv (C) The esultant of the othe foces is towads the cente. (D) The esultant of the othe foces vaies in magnitude as well as in diection. EXECISE-. A paticle of mass m begins to slide down a fixed smooth sphee fom the top. What is its tangential acceleation when it beaks off the sphee? g (B) 5g (C) g (D) g Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 0 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

7 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on A kg stone at the end of m long sting is whiled in a vetical cicle at constant speed of 4 m/sec. The tension in the sting is 6 N when the stone is at (g = 0 m/sec ) : top of the cicle (B) bottom of the cicle (C) halfway down (D) none of these. A boy whils a stone in a hoizontal cicle.8 m above the gound by means of a sting. m long. The sting beaks and stone flies off hoizontally, stiking the gound 9. m away. The centipetal acceleation duing the cicula motion was: (use g = 9.8 m/s ) 94 m/s (B) 4 m/s (C) 88 m/s (D) 8 m/s 4. A paticle of mass m is suspended fom a fixed point O by a sting of length l. At t = 0, it is displaced fom equilibium position and eleased. The gaph, which shows the vaiation of the tension T in the sting with time t, may be : (B) (C) (D) 5. A paticle P is moving in a cicle of adius a with a unifom speed u. C is the cente of the cicle and AB is diamete. The angula velocity of P about A and C ae in the atio : : (B) : (C) : (D) 4 : 6. The distance of the two planets fom the sun ae nealy 0 to 0 metes espectively. Then the atio of thei peiodic time, if they ae supposed to move in a cicula obit is : 0 : (B) : 0 (C) 0 0 : (D) : A stone of mass kg tied to a light inextensible sting of length L = m, whiling in a cicula path in a vetical plane. The atio of maximum tension in the sting to the minimum tension in the sting is 4, If g is taken to be 0 m/s, the speed of the stone at the highest point of the cicle is : 0 m/s (B) 5 m/s (C) 0 m/s (D) 0 m/s 8. Toy cat tied of the end of an unstetched sting of length a, when evolved moves in a hoizontal cicle of adius a with a time peiod T. Now the toy cat is speeded up until it moves in a hoizontal cicle of adius a with a peiod T. If Hook s law holds then : T = T (B) T = T (C) T = T (D) T = T 9. A small sphee of mass m suspended by a thead is fist taken aside so that the thead foms the ight angle with the vetical and then eleased, then : (i) The total acceleation of the sphee and the thead tension as a function of θ, the angle of deflection of the thead fom the vetical will be (ii) (iii) (A*) (C) g + cos θ, T = mg cos θ (B) g cos θ, T = mg cos θ. g + sin θ, T = 5mg cos θ (D) g sin θ, T = 5 mg cos θ. The thead tension at the moment when the vetical component of the sphee s velocity is maximum will be mg mg (B) mg (C*) mg (D) The angle θ between the thead and the vetical at the moment when the total acceleation Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

8 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on cos θ = vecto of the sphee is diected hoizontally will be (B) cos θ = (C) sin θ = (D) sin θ = 0. The kinetic enegy k of a paticle moving along a cicle of adius depends on the distance coveed s as k = as whee a is a constant. The total foce acting on the paticle is : a s (B) as / s + (C) as (D) a s. Two small sphees, each of mass m ae igidly connected by a od of negligible mass and ae eleased fom est in the position shown and slide down a smooth cicula guide in the vetical plane. x m y m A 45 m (i) Thei common velocity as they each the hoizontal dashed position will be : g g (B) 0 g g (C) g (D) g / (ii) The foce between sphee and the suppoting suface at an instant just befoe the sphee eaches the bottom position A will be :.9 mg (B).9 mg (C) mg (D) mg/. A paticle moves with deceleation along the cicle of adius so that at any moment of time its tangential and nomal acceleations ae equal in moduli. At the initial moment t = 0 the speed of the paticle equals v 0, then : (i) the speed of the paticle as a function of the distance coveed s will be v = v 0 e s/ (B) v = v 0 e s/ (C) v = v 0 e /s (D) v = v 0 e /s (ii) the total acceleation of the paticle as function of velocity and distance coveed a = v (B) a = v (C) a = m (D) a = v. A paticle A moves along a cicle of adius = 50 cm so that its adius vecto elative to the point O (Fig.) otates with the constant angula velocity ω = 0.40 ad/s. Then modulus of the velocity of the paticle, and the modulus of its total acceleation will be v = 0.4 m/s, w = 0.4 m/s (B) v = 0. m/s, w = 0. m/s (C) v = 0. m/s, w = 0.4 m/s (D) v = 0.4 m/s, w = 0. m/s 4. A spot light S otates in a hoizontal plane with a constant angula velocity of 0. ad/s. The spot of light P moves along the wall at a distance m. What is the velocity of the spot P when θ = 45 0? 0.6 m/s (B) 0.5 m/s (C) 0.4 m/s (D) 0. m/s v Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

9 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on EXECISE-4. A smooth od PQ otates in a hoizontal plane about its mid point M which is h = 0. m vetically below a fixed point A at a constant angula velocity 4 ad/s. A light elastic sting of natual length 0. m equiing.47 N/cm has one end fixed at A and its othe end attached to a ing of mass m = 0. kg which is fee to slide along the od. When the ing is stationay elative to od, then inclination of sting with vetical, tension in sting, foce exeted by ing on the od will be cos θ = /5, T = 9.8 N, N =.88 N (C) cos θ = /5, T = 4.9 N, N =.44 N. Figue shows the total acceleation and velocity of a paticle moving clockwise in a cicle of adius.5 m at a given instant of time. At this instant, find : (a) the adial acceleation, (b) the speed of the paticle and (c) its tangential acceleation (B) θ = 60, T = 0, N =.44 N (D) θ = 0, T = 0, N =.88 N. Two paticle A and B move anticlockwise with the same speed v in a cicle of adius and ae diametically opposite to each othe. At t = 0, A is given a constant acceleation (tangential) a t = 7v. Calculate the time 5π in which A collides with B, the angle taced by A, its angula velocity and adial acceleation at the time of collision. 4. A motocycle has to move with a constant speed on an ovebidge which is in the fom of a cicula ac of adius and has a total length L. Suppose the motocycle stats fom the highest point. (a) What can its maximum velocity be fo which the contact with the oad is not boken at the highest point. (b) If the motocycle goes at speed / times the maximum found in pat (a) whee will it lose the contact with the oad. (c) What maximum unifom speed can it maintain on the bidge if it does not lose contact anywhee on the bidge? 5. A 4 kg block is attached to a vetical od by means of two stings of equal length. When the system otates about the axis of the od, the stings ae extended as shown in figue. (a) How many evolutions pe minute must the system make in ode fo the tension in the uppe chod to be 0 kgf? (b) What is the tension in the lowe chod then? 6. A metallic chain with a length l and whose ends ae joined togethe is fitted onto a wooden disc as shown in the figue. The disc otates with a speed of n evolutions pe second. Find the tension of the chain T if its mass is m. Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

10 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on 7. A small object of mass m is tied to a sting of length l and is whiled ound in a hoizontal cicle of adius at constant speed v (figue). The cente of the cicle is vetically below the point of suppot. [This aangement is called conical pendulum.] Calculate v in tems of g, and θ. Also calculate the peiod of evolution. 8. A ca goes on a hoizontal cicula oad of adius, the speed inceasing at a constant ate dv = a. The fiction coefficient between the oad and the tye is µ. Find the speed at which the ca will dt skid. 9. A tack consists of two cicula pats ABC and CDE of equal adius 00 m and joined smoothly as shown in fig. Each pat subtends a ight angle at its cente. A cycle weighing 00 kg togethe with the ide tavels at a constant speed of 8 km/h on the ack. Find the nomal contact foce by the oad on the cycle when it is at B and D. (B) Find the coce of fiction exeted by the tack on the tyes when the cycle is at B, C and D. (c) Find the nomal foce between the oad and the cycle just, befoe and just afte the cycle cosses C. (D) What should be the minimum fiction coefficient between the oad and the tye, which will ensue that the cyclist can move with constant speed? Take g = 0m/s. 0. A block of mass m moves on a hoizontal cicle against the wall of a cylindical oom of adius. The floo of the oom on which the block moves is smooth but the fiction coefficient between the wall and the block is µ. The block is given an initial speed v 0. As a function of the instantaneous speed v wite (B) (C) (D) the nomal foce by the wall on the block, the fictional foce by the wall and the tangential acceleation of the block. obtain the speed of the block afte one evolution.. A table with smooth hoizontal suface is fixed in a cabin that otates with a unifom angula velocity ω in a cicula path of adius (figue). A smooth goove AB of length L(< < ) is made on the suface of the table.the goove makes an angle θ with the adius OA of the cicle in which the cabin otates. A small paticle is kept at the point A in the goove and is eleased to move along AB. Find the time taken by the paticle to each the point B.. A ca moving at a speed of 6 km/h is taking a tun on a cicula oad of adius 50 m. A small wodden plate is kept on the seat with its plane pependicula to the adius of the cicula oad figue. A small block of mass 00g is kept on the seat which ests against the plate. The fiction coefficient between the block and the plate is µ = Find the nomal contact foce exeted by the plate on the block. (B) The plate is slowly tuned so that the angle between the nomal to the plate and adius of the angle Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 4 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

11 Get Solution of These Packages & Lean by Video Tutoials on between the nomal to the plate and the adius of the oad slowly inceases. Find the angle at which the block will just stat sliding on the plate. FEE Download Study Package fom website: & A table with smooth hoizontal suface is placed in a cabin which moves in a cicle of a lage adius (figue). A smooth pulley of small adius is fastended to the table. Two masses m and m placed on the table ae conneted though a sting ove the pulley. Initially the masses ae held by a peson with the sting along the outwad adius and then the system is eleased fom est (with espect to the cabin). Find the magnitude of the initial acceleation of the masses as seen fom the cabin and the tension in the sting. EXECISE-5. A hemispheical bowl of adius = 0.m is otating about its axis (which is vetical) with an angula velocity ω. A paticle of mass 0 - kg on the fictionless inne suface of the bowl is also otating with the same ω. the paticle is at a height h fom the bottom of the bowl. (a) Obtain the elation between h and ω. What is the minimum value of ω needed in ode to have a nonzeo value of h. (b) It is desied to measue g using this setup by measuing h accuately. Assuming that and ω ae known pecisely and that the least count in the measuement of h is 0-4 m. What is minimum eo g in the measued value of g.[g = 9.8m/s ] [JEE 99]. A paticle of mass m is moving in a cicula path of constant adius such that is centipetal acceleation a c is vaying with time t as a c = k t whee k is a constant. The powe deliveed to the paticle by the foce acting on it is- [JEE 994] 4 5 (mk t ) π mk (B) mk t (C) (D) Zeo. A smooth semicicula wie tack of adius is fixed in a vetical plane (figue). On end of a massless sping of natual length /4 is attached to the lowest point O of the wie tack. A small ing of mass m which can slide on the tack is attached to the othe end of the sping. The ing is held stationay at point P such that the sping make an angle 60 with the vetical. The sping constant K = mg/. Conside the instant when the ing is eleased (i) Daw the fee body diagam of the ing. (ii) Detemine the tangential acceleation of the ing and the nomal eaction. [JEE 996] 4. Two blocks of mass m = 0 Kg and m = 5 Kg connected to each othe by a massless inextensible sting of length 0. m ae placed along a diamete of tun table. The coefficient of fiction between the table and m is 0.5 while thee is no fiction between m and the table. The table is otating with an angula velocity of 0 ad/s about a vetical axis passing though its cente O. The masses ae placed along the diamete of the table on eithe side of the cente O such that the mass m is at a distance of 0.4 m fom O. The masses ae obseved to be at est with espect to an obseve on the tun table. (i) Calculate the fictional foce on m. (ii) What should be the minimum angula speed of the tun table so that the masses will slip Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 5 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

12 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on fom this position. (iii) How should the masses by placed with the sting emaining taut so that thee is no fictional foce acting on the mass m. [JEE 997] 5. A small block of mass m slides along a smooth fictional tack as shown in figue. (i) If it stats fom est at P, when is the esultant foce acting on it at Q? (ii) At what height above the bottom of the loop should the block be eleased so that the foce it exets against the tack at the top of the loop equals its weight? [EE 997] 6. A stone tied to a sting of length L is whiled in a vetical cicle with the othe end of the sting at the cente. At a cetain instant of time the stone is at its lowest position and has a speed u. The magnitude of the change in its velocity as it eaches a position, whee the sting is hoizontal, is [JEE 998] u gl (B) gl (C) u gl (D) (u gl) 7. A paticle at est stats olling fom the top of a lage fictionless sphee of adius. The sphee is fixed on the gound. Calculate that height fom the gound at which the paticle leaves the suface of the sphee. [EE 998] 8. A paticle is suspended vetically fom a point O by an inextensible massless sting of length L. A vetical line AB is at a distance L/8 fom O as shown. The object given a hoizontal velocity u. At some point, its motion ceases to be cicula and eventually the object passes though the line AB. At the instant of cossing AB, its velocity is hoizontal. Find u. O L u L/8 A B [JEE 999] 9. A long hoizontal od has a bead which can slide along its length and is initially placed at a distance L fom one end A of the od. The od is set in angula motion about A with a constant angula acceleation, α. If the coefficient of fiction between the od and the bead is µ, and gavity is neglected, then the time afte which the bead stats slipping is - [JEE 000] µ α (B) µ α (C) µα (D) Infinitesimal 0. A small block is shot into each of the fou tacks as shown below. Each of the tacks ises to the same height. The speed with which the block entes the tack is the same in all cases. At the highest point of the tack, the nomal eaction is maximum is- [JEE 00] (B) (C) (D). An insect cawls up a hemispheical suface vey slowly (see the figue). The coefficient of fiction between the suface and the insect is /. If the line joining the cente of the hemispheical suface to the insect makes an angle α with the vetical, the maximum possible value of α is given- cot α = (B) tan α = (C) sec α = (D) cosec α = [JEE 00] Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 6 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

13 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on A block is placed inside a hoizontal hollow cylinde. The cylinde stats otating with one evolution pe second about its axis. The angula position of the block at which it begins to slide is 0 below the hoizontal level passing though the cente. Find the adius of the cylinde if the coefficient of fiction is 0.6. What should be the minimum angula speed of the cylinde so that the block each the highest point of the cylinde? [EE 00]. A simple pendulum is oscillating without damping. When the displacements of the bob is less than maximum, its acceleation vecto a is coectly shown in [JEE 00] (B) (C) (D) 4. A spheical ball of mass m is kept at the highest point in the space between two fixed, concentic sphees A and B (see figue). The smalle sphee A has a adius and the space between the two sphees has a width d. The ball has a diamete vey slightly less than d. All sufaces ae fictionless. The ball given a gentle push (towads the ight in the figue). The angle made by the adius vecto of the ball with the upwad vetical is depended by θ (shown in figue) (a) Expess the total nomal eaction foce exeted by the sphees on the ball as a function of angle θ. (b) Let N A and N B denote the magnitudes of the nomal eaction foce on the ball extoted by the sphees A and B, espectively. Sketch the vaiations of N A and N B as functions of cosθ in the ange 0 θ π by dawing two sepaate gaphs in you answe book, taking cosθ on the hoizontal axis d q O Sphee Sphee ¼xksy k½ ¼xksy k½ B A [JEE 00] 5. A double sta system consists of two stas A and B which have time peiod T A and T B. adius A and B and mass M A and M B. Choose the coect option. [IIT 006, (, ] If T A > T B then A > B (B) If T A > T B then M A > M B T (C) T A B = A B (D) T A = T B Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 7 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

14 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on EXECISE # SECTION : KINEMATICS OF CICULA CULA MOTION A. (b) fist (b) thid. SECTION ( B ) : AD IAL AND T ANGENTIAL ACCELEA ATION B..7 m/sec SECTION (C ) : AD IUS OF CUVATUE AND DYNAMICS OF CICULA CULA MOTION C. 8 T C C. u cos θ gcos ( θ/ ) C 4. [4.8N, 4.8 N] SECTION (D) : CICULA CULA MOTION IN HOIZONTAL PLANE D. 0 ad/s D. 4.5 mg D. m/s D SECTION ( E) : CICULA MOTION IN V E TICAL PLANE E. (i) h min = 5 (ii) F = 6 mg E. 0.8 m E. 4 m/sec SECTION ( F) : M OTION OF A V E HICLE, CE NTIFUGAL FOF OCE AND OTATION TION OF EATH F. 4.5 cm F. v = ω F. tan (/4)] F F , (B).0 hou] F 6. Between 4.7 km/h and 54 km/h] EXECISE # SECTION : KINEMATICS OF CICULA CULA MOTION A. D A. C A. D A 4. AD A 5. D A 6. BD SECTION ( B ) : AD IAL AND T ANGENTIAL ACCELEA ATION B. C B. D B. D B 4. D B 5. C B 6. A B 7. B B 8. D B 9. C SECTION (C ) : AD IUS OF CUVATUE AND DYNAMICS OF CICULA CULA MOTION C. D C. A SECTION (D) : CICULA CULA MOTION IN HOIZONTAL PLANE D. D D. D D. A D 4. A D 5. A SECTION ( E) : CICULA MOTION IN V E TICAL ANSWE PLANE E. C E. A E. B E 4. D E 5. B E 6. C E 7. C E 8. C E 9. D SECTION ( F) : M OTION OF A V E HICLE, CE NTIFUGAL FOF OCE AND OTATION TION OF EATH F. A F. C F. D F 4. A F 5. BC F 6. BD F 7. BD EXECISE #. B. A. C 4. D 5. B 6. D 7. A 8. B 9. (i) A (ii) C (iii) A 0. B. (i) A (ii) B. (i) A (ii) A. D 4. A EXECISE # 4. A. (a).65 m/s (b) 7.5 m/s (c).5 m/s. 5π π,, 6v 6 7 v 89v, (a) v max = g, (b) At angle θ = 60º fom the vetical position. (c) v = gcos L 5. (a) 9.6 pe min., (b) 50 N 6. T = mln 7. g tanθ, π gtanθ 8. Net foce on ca = fictional foce f 4 v f = m a + (whee m is mass of the ca)...() Fo skidding to just occu f = µn = µmg...() Fom () and () v = / 4 { [ µ g a ]} [( µ g a ) ] N, 05 N, (B) 0,707N, 0, (C) 68N, 7 N, (D ) 0.07] Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 8 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.

15 FEE Download Study Package fom website: & Get Solution of These Packages & Lean by Video Tutoials on EXECISE # 5 0. (B) (i) (ii) (iii) (iv) The nomal eaction by wall on the mv block is N = The fiction foce on the block by the µmv wall is f = µn = The tangential acceleation of the block = m f = dv µv = dt o π µ = ds 0 integating we get Ans. (B) ln v 0 µv v dv µv dv v = ds v v 0 v = µ π o v = v 0 e µπ (i) mv (ii) µv (iii) (iv) v 0 e πµ. L ω cosθ. 0.N, (B) 0º ω. 4. mω µmv. (a) 7 ad/ s (b) -9.8 x 0 - m/s. B. (i) (ii) a T = (i) 6 N (ii).67 ad/s (iii) = 0. m and = 0. m 5. ( 65 ) mg, 6. D 7. H = (5/) A 0. A. A. 0.4m,6.4ad/sec. C 4. (a) N = mg cosθ - mg, (b) 5. D mg N A cosθ cos θ=/ cos θ= 5mg N B cos θ= g, N = mg 8 u = gl + cos θ=/ cosθ Teko Classes, Maths : Suhag. Kaiya (S.. K. Si), Bhopal Phone : , page 9 Successful People eplace the wods like; "wish", "ty" & "should" with "I Will". Ineffective People don't.