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JEE-Physics Node-6\E:\Data\2014\Kota\JEE-Advanced\SMP\Phy\NLM\English\Exercise.p65 E 51 EXERCISE–01 CHECK YOUR GRASP SELECT THE CORRECT ALTERNATIVE (ONLY ONE CORRECT ANSWER) 1 . A body of mass m1 exerts a force on another body of mass m2 . If the magnitude of acceleration of m2 is a2 , then the magnitude of the acceleration of m1 is (considering only two bodies in space) (A) Zero (B) 2 2 1 m a m (C) 1 2 2 m a m (D) a2 2 . A monkey is descending from the branch of a tree with constant acceleration. If the breaking strength of branch is 75% of the weight of the monkey, the minimum acceleration with which the monkey can slide down without breaking the branch is (A) g (B) 3g 4 (C) g 4 (D) g 2 3 . A trolley of mass 5 kg on a horizontal smooth surface is pulled 5kg 2kg C A B by a load of mass 2 kg by means of uniform rope ABC of length 2 m and mass 1 kg. As the load falls from BC=0 to BC=2m. its acceleration in m/s2 changes– (A) 20 6 to 20 5 (B) 20 8 to 30 8 (C) 20 5 to 30 6 (D) None of the above 4 . In the figure, the position–time graph of a particle of X(m) 4 6 2 2 4 6 t(sec) mass 0·1 kg is shown. The impulse at t=2 second is (A) 0·2 kgms–1 (B) –0·2 kgms–1 (C) 0·1 kgms–1 (D) –0·4 kgms–1 5 . Figures I, II, III and IV depicts variation of force with time 1 t(ms)  F(N) 0·25 1 2 t(ms)  F(N) 0·3 (I) (II) 1 t(ms)  F(N) 1 1 t(ms)  F(N) 1 (III) (IV) In which situation impulse will be maximum (A) I & II (B) III & I (C) III & IV (D) Only IV 6 . A body kept on a smooth inclined plane inclination 1 in x will remain stationary relative to the inclined plane if the plane is given a horizontal acceleration equal to :– (A) 2 x 1g  (B) 2 x 1 g x  (C) 2 gx x 1 (D) 2 g x 1 7 . A monkey is sitting on the pan of a spring balance which is placed on an elevator. The maximum reading of the spring balance will be when : (A) the elevator is stationary (B) the string of the elevator breaks and it drops freely towards the earth (C) the elevator is accelerated downwards (D) the elevator is accelerated upwards.
JEE-Physics Node-6\E:\Data\2014\Kota\JEE-Advanced\SMP\Phy\NLM\English\Exercise.p65 52 E 8 . A pulley is attached to the ceiling of a lift moving upwards. Two particles are attached to the two ends of a string passing over the pulley. The masses of the particles are in the ratio 2 : 1. If the acceleration of the particles is g/2, then the acceleration of the lift will be (A) g (B) g 2 (C) g 3 (D) g 4 9 . Two blocks A and B of masses m & 2m respectively are held at rest such that the spring is in natural length. What is the acceleration of both the blocks just after release? (A) g , g  (B) g 3 , g 3  (C) 0, 0 (D) g  , 0 m A B 2m 1 0 . In the arrangement shown in figure, pulley is smooth and massless and all the strings are light. Let F1 be the force exerted on the pulley in case (i) and F2 the force in case (ii). Then (A) F1 > F2 2m 4m m (i) (ii) m 4m (B) F1 < F2 (C) F1 = F2 (D) F1 = 2F2 1 1 . In the figure, the blocks A, B and C of mass m, each have accelerations a1 , a2 and a3 respectively. F1 and F2 are external forces of magnitudes 2mg and mg respectively. (A) a1 = a2 = a3 m A F=2mg 1 m B 2m m C m F=mg 2 (B) a1>a 3>a 2 (C) a1=a2, a2>a 3 (D) a1>a2, a2=a 3 1 2 . In the arrangement shown in figure m1 = 1kg, m2 = 2kg. Pulleys are massless and strings are light. For what value of M the mass m1 moves with constant velocity ( Neglect friction) (A) 6 kg (B) 4 kg M 1 2 m2 m1 (C) 8 kg (D) 10 kg 1 3 . A trolley is being pulled up an incline plane by a man sitting on it (as 15° shown in figure). He applies a force of 250 N. If the combined mass of the man and trolley is 100 kg, the acceleration of the trolley will be [sin15° = 0.26] (A) 2.4 m/ s2 (B) 9.4 m/s2 (C) 6.9 m/s2 (D) 4.9 m/s2 1 4 . A man thinks about 4 arrangements as shown to raise two small bricks each having mass m. Which of the arrangement would take minimum time? (A) F m m (B) m m F (C) m m F (D) m m F
JEE-Physics Node-6\E:\Data\2014\Kota\JEE-Advanced\SMP\Phy\NLM\English\Exercise.p65 E 53 1 5 . In the arrangement shown in figure neglect the masses of the pulley and string and also friction. The accelerations of blocks A and B are (A) g, g/2 m2 m1 C A B (B) g/2, g (C) 3g/2, 3g/4 (D) g, g 1 6 . A block is placed on an inclined plane moving towards right horizontally with A 30° B C a=g 0 an acceleration a0 = g. The length of the plane AC = 1m. Friction is absent everywhere. The time taken by the block to reach from C to A is ( g = 10 m/s2) (A) 1.2 s (B) 0.74 s (C) 2.56 s (D) 0.42 s 1 7 . In the arrangement shown in figure pulley A and B are massless and the thread is inextensible. Mass of pulley C is equal to m. If friction in all the pulleys is negligible, then (A) tension in thread is equal to 1/2 mg B A C (B) acceleration of pulley C is equal to g/2 (downward) (C) acceleration of pulley A is equal to g/2 (upward) (D) acceleration of pulley A is equal to 2g (upward) 1 8 . A block is placed on a rough horizontal plane. A time dependent horizontal force F = kt acts on the block. Here k is a positive constant. Acceleration–time graph of the block is (A) a t (B) a t (C) a t (D) a t 1 9 . In the figure shown if friction coefficient of block 1kg and 2kg with inclined plane is μ1 =0.5 and μ2 = 0.4 respectively, then (A) both block will move together )60° 2kg 1kg (B) both block will move separately (C) there is a non zero contact force between two blocks (D) None of these 2 0 . A block of mass of 10 kg lies on a rough inclined plane of inclination = sin–1 3 5        O A B C D 30N with the horizontal when a force of 30N is applied on the block parallel to and upward the plane, the total force exerted by the plane on the block is nearly along (coefficient of friction is μ = 3 4 ) ( g = 10 m/s2) (A) OA (B) OB (C) OC (D) OD
JEE-Physics Node-6\E:\Data\2014\Kota\JEE-Advanced\SMP\Phy\NLM\English\Exercise.p65 54 E 2 1 . A block of mass 3 kg is at rest on a rough inclined plane as shown in the figure. The magnitude of net force exerted by the surface on the block will be (g=10 m/s2 ) 30o 3 kg (A) 26N (B) 19.5N (C) 10N (D) 30 N 2 2 . A block of mass m = 2 kg is resting on a rough inclined plane of inclination 300 as shown in figure. The coefficient of friction between the block and the plane is μ = 0.5. What minimum force F should be applied perpendicular to the plane on the block, so that block does not slip on the plane (g=10m/s2 ) A F 30° (A) zero (B) 6.24 N (C) 2.68 N (D) 4.34 N 2 3 . A block of mass 0.1 kg is held against a wall applying a horizontal force of 5N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is :– (A) 2.5 N (B) 0.98 N (C) 4.9 N (D) 0.49 N 2 4 . A 40 kg slab rests on a frictionless floor. A 10 kg block rests on top of the slab. The static coefficient of friction between the block and slab is 0.60 while the kinetic coefficient is 0.40. The 10 kg block is acted upon by a horizontal force o f 100N. If g = 9.8 m/s 2 , the resulting acceleration of the slab will be :– 10kg 40kg 100N No Friction (A) 0.98 m/s2 (B) 1.47 m/s2 (C) 1.52 m/s2 (D) 6.1 m/s2 2 5 . The rear side of a truck is open and a box of mass 20 kg is placed on the truck 4m away from the open end,  = 0.15 and g=10 m/sec2 . The truck starts from rest with an acceleration of 2m/sec2 on a straight road. The distance moved by the truck when box starts fall down. (A) 4 m (B) 8 m (C) 16 m (D) 32 m 2 6 . In the arrangement shown in figure, coefficient of friction between the two blocks is μ = 1 2 . The force of friction acting between the two blocks is 2kg 4kg F=2N 1 F=20N 2 (A) 8 N (B) 10 N (C) 6 N (D) 4 N 2 7 .  is the angle of the incline when a block of mass m just starts slipping down. The distance covered by the block if thrown up the incline with an initial speed v0 is : (A) 2 0 v 4g sin  (B) 2 4v 0 g sin  (C) 2 0 v sin 4g  (D) 2 4v sin 0 g 