10. The dimensional formula for c) 6% d) 7%

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1 UNIT. One of the combinations from the fundamental phsical constants is hc G. The unit of this epression is a) kg b) m 3 c) s - d) m. If the error in the measurement of radius is %, then the error in the determination of volume of the sphere will be a) 8% b) % c) 4% d) 6% NATURE OF PHYSICAL WORLD AND MEASUREMENT 3. If the length and time period of an oscillating pendulum have errors of % and 3% respectivel then the error 9. The velocit of a particle v at an instant t is given b v = at + bt. The dimensions in measurement of acceleration due to of b is gravit is a) [L] b) [LT - ] a) 4% [Related to AMPMT 008] c) [LT - ] d) [LT -3 ] b) 5% 0. The dimensional formula for c) 6% d) 7% gravitational constant G is [Related to AIPMT 004] 4. The length of a bod is measured as 3.5 m, if the accurac is 0.0mm, then the percentage error in the measurement is a) 35% b) % c) 0.8% d) 0.035% 5. Which of the following has the highest number of significant figures? a) m b) kg c) m d) J 6. If π = 3.4, then the value of π is a) b) c) 9.86 d) Which of the following pairs of phsical quantities have same dimension? a) force and power b) torque and energ c) torque and power d) force and torque 8. The dimensional formula of Planck's constant h is [AMU, Main, JEE, NEET] a) [ML T - ] b) [ML T -3 ] c) [MLT - ] d) [ML 3 T -3 ] a) [ML 3 T - ] b) [M - L 3 T - ] c) [M - L -3 T - ] d) [ML -3 T ]. The densit of a material in CGS sstem of units is 4 g cm -3. In a sstem of units in which unit of length is 0 cm and unit of mass is 00 g, then the value of densit of material will be a) 0.04 b) 0.4 c) 40 d) 400. If the force is proportional to square of velocit, then the dimension of proportionalit constant is [JEE-000] a) [MLT 0 ] b) [MLT - ] c) [ML - T] d) [ML - T 0 ] Page of

2 3. The dimension of με 0 0 [Main AIPMT 0] (a) length time (c) velocit (d) force ( ) is 4. Planck s constant (h), speed of light in vacuum (c) and Newton s gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length?. [NEET 06 (phase II)] (a) hg 3 c hg 5 c (c) hc G (d) Gc 3 h 5. A length-scale (l) depends on the permittivit ( ) of a dielectric material, Boltzmann constant (k B ), the absolute temperature (T), the number per unit volume (n) of certain charged particles, and the charge (q) carried b each of the particles. Which of the following epression for l is dimensionall correct?. [JEE (advanced) 06] (a) l = nq εkt B kt B l = ε nq (c) l = (d) l = q 3 εnkt B q εnk T B Page of

3 UNIT KINEMATICS I. Multi Choice Question. Which one of the following Cartesian coordinate sstems is not followed in phsics? z (a) (c) z z (d) z. Identif the unit vector in the following. (a) 77.3 m 78.4 m ˆ (a) î ˆ i (c) 80.5 m (d) 79. m j ˆ (c) ˆ j iˆ ˆj 8. A ball is projected verticall upwards k (d) with a velocit v. It comes back to ground in time t. Which v-t graph shows the 3. Which one of the following phsical motion correctl? (NSEP 00-0) quantities cannot be represented b a scalar? (a) Mass length (c) momentum (d) magnitude of acceleration 4. Two objects of masses m and m fall from the heights h and h respectivel. The ratio of the magnitude of their momenta when the hit the ground is (AIPMT 0) 5. If a particle has negative velocit and negative acceleration, its speed (a) increases decreases (c) remains same (d) zero 6. If the velocit is v i ˆ t ˆ j 9k, then the magnitude of acceleration at t = 0.5 s is (a) m s - m s - (c) zero (d) - m s - 7. If an object is dropped from the top of a building and it reaches the ground at t = 4 s, then the height of the building is (ignoring air resistance) (g = 9.8 ms ) v v (a) (c) t t v v (d) t t (a) (c) m m h h h h (d) m m mh mh Page 3 of

4 9. If one object is dropped verticall downward and another object is thrown horizontall from the same height, then the ratio of vertical distance covered b both objects at an instant t is (a) (c) 4 (d) A ball is dropped from some height towards the ground. Which one of the following represents the correct motion of the ball? (a). If a particle eecutes uniform circular motion, choose the correct statement (NEET 06) (a) The velocit and speed are constant. The acceleration and speed are constant. (c) The velocit and acceleration are constant. (d) The speed and magnitude of acceleration are constant. 3. If an object is thrown verticall up with the initial speed u from the ground, then the time taken b the object to return back to ground is (a) u g u g (c) u g 4. Two objects are projected at angles 30 and 60 respectivel with respect to the (c) (d). If a particle eecutes uniform circular motion in the plane in clock wise direction, then the angular velocit is in (a) + direction +z direction (c) -z direction (d) - direction (d) u g horizontal direction. The range of two objects are denoted as R 30 0 and R Choose the correct relation from the following (a) R 30 0 = R 60 0 R R 60 0 (c)r 30 0 = R 60 0 (d) R 30 0 = R An object is dropped in an unknown planet from height 50 m, it reaches the ground in s. The acceleration due to gravit in this unknown planet is (a) g = 0 m s - g = 5 m s - (c) g = 5 m s - (d) g = 30 m s - Page 4 of

5 UNIT 3 I. Multiple Choice Questions. When a car takes a sudden left turn in the curved road, passengers are pushed towards the right due to (a) inertia of direction inertia of motion (c) inertia of rest (d) absence of inertia. An object of mass m held against a vertical wall b appling horizontal force F as shown in the figure. The minimum value of the force F is (IIT JEE 994) (a) Less than mg Wall Equal to mg (c) Greater than mg (d) Cannot determine F m LAWS OF MOTION 4. A book is at rest on the table which eerts a normal force on the book. If this force is considered as reaction force, what is the action force according to Newton s third law? (a) Gravitational force eerted b Earth on the book Gravitational force eerted b the book on Earth (c) Normal force eerted b the book on the table (d) None of the above 5. Two masses m and m are eperiencing the same force where m m <. The ratio of their acceleration a is a (a) 3. A vehicle is moving along the positive direction, if sudden brake is applied, less than then (a) frictional force acting on the (c) greater than (d) all the three cases vehicle is along negative 6. Choose appropriate free bod diagram direction for the particle eperiencing net frictional force acting on the acceleration along negative direction. vehicle is along positive direction (Each arrow mark represents the force (c) no frictional force acts on the acting on the sstem). vehicle (d) frictional force acts in downward direction a) b) c) d) Page 5 of

6 7. A particle of mass m sliding on the smooth double inclined plane (shown in figure) will eperience (a) greater acceleration along the path AB greater acceleration along the path AC (c) same acceleration in both the paths (d) no acceleration in both the paths. 8. Two blocks of masses m and m are placed on a smooth horizontal surface (d) onl kinetic friction acts on the object as shown. In the first case onl a force. When an object is at rest on the inclined F is applied from the left. Later onl a rough surface, force F is applied from the right. If the (a) static and kinetic frictions acting force acting at the interface of the two on the object is zero blocks in the two cases is same, then static friction is zero but kinetic F: Fis friction is not zero (Phsics Olmpiad 06) (c) static friction is not zero and kinetic friction is zero (d) static and kinetic frictions are not zero 3. The centrifugal force appears to eist (a) : : (c) : (d) :3 (a) onl in inertial frames 9. Force acting on the particle moving with constant speed is (a) alwas zero need not be zero (c) alwas non zero (d) cannot be concluded 0. An object of mass m begins to move on the plane inclined at an angle. The coefficient of static friction of inclined surface is m s. The maimum static friction eperienced b the mass is (a) mg m s mg (c) m s mg sin (d) m s mg cos. When the object is moving at constant velocit on the rough surface, (a) net force on the object is zero no force acts on the object (c) onl eternal force acts on the object onl in rotating frames (c) in an accelerated frame (d) both in inertial and non-inertial frames Page 6 of

7 4. Choose the correct statement from the following (a) Centrifugal and centripetal forces are action reaction pairs Centripetal forces is a natural force (c) Centrifugal force arises from gravitational force (d) Centripetal force acts towards the center and centrifugal force appears to act awa from the center in a circular motion 5. If a person moving from pole to equator, the centrifugal force acting on him (a) increases decreases (c) remains the same (d) increases and then decreases Page 7 of

8 UNIT 4 WORK, ENERGY AND POWER. A uniform force of (î + ˆj) N acts on a particle of mass kg. The particle displaces from position (3 ĵ kˆ ) m to (5ˆ i 3ˆ j) m. The work done b the force on the particle is (AIPMT model 03) (a) 9 J 6 J (c) 0 J (d) J. A ball of mass kg and another of mass kg are dropped from a tall building whose height is 80 m. After, a fall of 40 m each towards Earth, their respective kinetic energies will be in the ratio of (AIPMT model 004) (a) : : (a) b the sstem against a conservative force (c) : (d) : b the sstem against a nonconservative force 3. A bod of mass kg is thrown upwards with a velocit 0 m s. It momentaril comes to rest after attaining a height of (c) upon the sstem b a conservative force 8 m. How much energ is lost due to (d) upon the sstem b a nonconservative air friction?. force (Take g = 0ms ) (AIPMT 009) (a) 0 J 30 J (c) 40 J (d) 0 J 4. An engine pumps water continuousl through a hose. Water leaves the hose with a velocit v and m is the mass per unit length of the water of the jet. What is the rate at which kinetic energ is imparted to water?. (AIPMT 009) (a) mv mv 3 (c) 3 mv (d) 5 mv 5. A bod of mass 4 m is ling in -plane at rest. It suddenl eplodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energ generated due to eplosion is (AIPMT 04) (a) mv 3 mv (c) mv (d) 4mv 6. The potential energ of a sstem increases, if work is done 7. What is the minimum velocit with which a bod of mass m must enter a vertical loop of radius R so that it can complete the loop?. (a) gr 3gR (c) 5gR (d) gr 8. The work done b the conservative force for a closed path is (a) alwas negative zero (c) alwas positive (d) not defined Page 8 of

9 9. If the linear momentum of the object is increased b 0.%, then the kinetic energ is increased b (a) 0. % 0.% (c) 0.4% (d) 0.0% 0. If the potential energ of the particle is, then force eperienced b a) U() U() b) U() U() c) d) the particle is (a) F 4. A particle which is constrained to F move along -ais, is subjected to a (c) F (d) F force in the same direction which varies with the distance of the particle. A wind-powered generator converts wind energ into electric energ. Assume that the generator converts a fied fraction of the wind energ intercepted b its blades into electrical from the origin as F k a. Here, k and a are positive constants. For 0, the functional form of the potential energ U() of the particle is (IIT 00) energ. For wind speed v, the electrical U() U() power output will be proportional to (a) v v a) b) (c) v 3 (d) v 4. Two equal masses m and m are moving along the same straight line with velocities 5ms - and 9ms - respectivel. If the collision is elastic, then calculate the velocities after the collision of m and m, respectivel (a) 4ms - and 0 ms - 0ms - and 0 ms - (c) 9ms - and 5 ms - (d) 5 ms - and ms - 3. A particle is placed at the origin and a force F k is acting on it (where k is a positive constant). If U 0 0, the graph of U versus will be (where U is the potential energ function) (IIT 004) c) U() d) U() 5. A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of (a) 3 k (c) 3k 3 k (d) 6k Page 9 of

10 UNIT 5 MOTION OF SYSTEM OF PARTICLES AND RIGID BODIES I. Multi Choice Question. The center of mass of a sstem of particles does not depend upon, (a) position of particles relative distance between particles (c) masses of particles (d) force acting on particle [AIPMT 997, AIEEE 004] (d) depends on direction of rotation.. A couple produces, [IIT 998] (a) pure rotation 6. A rigid bod rotates with an angular pure translation (c) rotation and translation momentum L. If its kinetic energ is halved, the angular momentum becomes, (d) no motion (a) L L/ [AIPMT 997] (c) L (d) L/ 3. A particle is moving with a constant [AFMC 998, AIPMT 05] velocit along a line parallel to positive 7. A particle undergoes uniform circular X-ais. The magnitude of its angular motion. The angular momentum of the momentum with respect to the origin is, (a) zero increasing with (c) decreasing with (d) remaining constant [IIT 00] 4. A rope is wound around a hollow clinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the clinder if the rope is pulled with a particle remain conserved about, (a) the center point of the circle. the point on the circumference of the circle. (c) an point inside the circle. (d) an point outside the circle. [IIT 003] 8. When a mass is rotating in a plane about a fied point, its angular momentum is directed along, force 30 N? (a) 0.5 rad s 5 rad s (c) 5 m s (d) 5 m s. [NEET 07] 5. A closed clindrical container is partiall filled with water. As the container rotates in a horizontal plane about a perpendicular bisector, its moment of inertia, (a) increases decreases (c) remains constant (a) a line perpendicular to the plane of rotation the line making an angle of 45 to the plane of rotation (c) the radius (d) tangent to the path [AIPMT 0] Page 0 of

11 9. Two discs of same moment of inertia rotating about their regular ais passing through center and perpendicular to the plane of disc with angular velocities ω and ω. The are brought in to contact face to face coinciding the ais of rotation. The epression for loss of energ during this process is, (a) (c) MR /3 (d) 9MR /3 4 I( ) I( ) [NEET 06] (c) 8 I( ) (d) 3. The speed of a solid sphere after rolling I( ) down from rest without sliding on an inclined plane of vertical height h is, [NEET 07] 4 0. A disc of moment of inertia I a is rotating (a) 3 gh 0 7 gh in a horizontal plane about its smmetr ais with a constant angular speed ω. Another discinitiall at rest of moment (c) gh (d) gh of inertia I b is dropped coaiall on to the rotating disc. Then, both the discs 4. The speed of the center of a wheel rotate with same constant angular rolling on a horizontal surface is v o. A speed. The loss of kinetic energ due to point on the rim in level with the center friction in this process is, will be moving at a speed of speed of, (a) Ib ( Ia + Ib) ω (a) zero v o Ib ( Ia + Ib) ω (c) v (d) v o o [PMT 99, PMT 003, IIT 004] ( Ib Ia) (c) ω 5. A round object of mass M and radius ( Ia + Ib) (d) R rolls down without slipping along II b b ω [AIPMT 00] an inclined plane. The fractional force, ( Ia + Ib) (a) dissipates kinetic energ as heat.. The ratio of the acceleration for a solid decreases the rotational motion. sphere (mass m and radius R) rolling (c) decreases the rotational and down an incline of angle θ without transnational motion slipping and slipping down the incline (d) converts transnational energ into without rolling is, rotational energ (a) 5:7 :3 (c) :5 (d) 7:5 [AIPMT 04]. From a disc of radius R a mass M, a circular hole of diameter R, whose rim passes through the center is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular ais passing through it (a) 5MR /3 3MR /3 [PMT 005] Page of

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