-: MECHANICS:- 2. Motion in one dimension & 3. Newton s laws of motion

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1 -: MECHANICS:- Chapters: 1.Units and Dimensions, 2. Motion in one dimension & 3. Newton s laws of motion 01. The quantities L/R and RC (where L, C and R stand for inductance, capacitance and resistance respectively) have the same dimensions as those of 1) Velocity 2) acceleration 3) time 4) force 02. Which of the following observers is inertial? 1) A child revolving in a merry-go-round 2) A driver in a car moving with a uniform velocity 3) A pilot in an aircraft which is taking off 4) A passenger in a train which is slowing down to stop 03. A train is going north at a speed of 10ms -1. A parrot flies at a speed of 2.5ms -1 towards south parallel to the railway track. If the time taken by the parrot to cross the train is 12s, the length of the train is 1) 90m 2) 150m 3) 120m 4) 30m 04. A dimensionless quantity 1) Never has a unit 2) Always has a unit 3) May have a unit 4) Does not exist 05. The splash is heard 2.05s after a stone is dropped into a well of depth19.6m.the velocity of sound is (g = 9.8 ms -2 ), 1) 352ms -1 2) 342ms -1 3) 392ms -1 4) 372ms An object may have (1) Varying speed without having varying velocity (2) Varying velocity without having varying speed (3) Non-zero acceleration without having varying speed The correct statements are 1) 1& 2 2) 2&3 3) 3&1 4) 1 only

2 07. Of the following pairs, which one does not have identical dimensions? 1) Moment of inertia & moment of force 2) work & torque 3) angular momentum & Planck s constant 4) impulse & linear momentum 08. A particle starting from rest moves with a constant acceleration a. If the acceleration depends on time as a= [bt]; b is constant, then displacement of the particle in the time interval t=0 to t=t 1 will be 2 3 1) 1/2 at 1 2) 1/2bt ) 1/6bt 1 4) 1/2bt When a horse pulls a cart, the force that helps the horse to move forward, is the force exerted by 1) The horse on the cart 2) the cart on the horse 3) the horse on the ground 4) the ground on the horse 10. A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force F is applied at the free end of the rope, the net force exerted on the block is 1) FM/ (M+m) 2) Fm/ (M+m) 3) Fm/ (M-m) 4) F 11. If a spring of Force constant k is cut into three equal parts, then the force constant of each part will be 1) k 2) 3 k 3) k /3 4) 6k 12. A force F is applied horizontally to a block A of mass m 1 which is in contact with a block B of mass m 2, as shown in the figure. If the surfaces are frictionless, the force exerted by A on B is given by Force A B Acceleration 1) (m 1 /m 2 ) F 2) (m 2 /m 1 ) F 3) m 1 F/ (m 1 +m 2 ) 4) m 2 F/ (m 1 +m 2 )

3 13. A rocket of mass 6 tons is set for vertical firing. If the exhaust speed be 1km per second how much gas must be ejected to give the rocket an upward acceleration of 20ms -2? (Take g = 9.8 ms -2 ) 1) 45kg/s 2) 90kg/s 3)120kg/s 4)180kg/s 14. A ball is released from the top of a tower of height h (m) and it takes T seconds to reach the ground. What is the position of the ball from the ground in T/4 seconds (in m)? 1) 15h/16 2) h/16 3) 9h/16 4) h 15. A player caught a cricket ball of mass 0.15kg moving at 20ms -1 in 0.1s. The force exerted by the ball on the hand of the player is 1) 3N 2) 30N 3) 300N 4) 150N 16. N bullets each of mass m kg are fired with a velocity v ms -1, at the rate of n bullets per second, upon a wall. The reaction offered by the wall to the bullets is 1) nnmv 2) Nmv/n 3) nnm/v 4) nnv/m 17. A shell explodes into 3 fragments of equal masses. Two fragments fly off at right angles to each other with speeds of 9ms -1 and 12ms -1. What is the speed of the third fragment (in ms -1)? 1) 9 2) 12 3) 15 4) Intensity of a wave is energy transmitted per unit area per second. The dimensional formula of intensity of a wave is 1) ML 0 T -2 2) ML 0 T -3 3) ML 0 T -1 4) ML 4 T 19. A ball is dropped from a height of 10m. It is embedded 1m in sand and stops. In this process 1) Only momentum is conserved 2) Only kinetic energy is conserved 3) Both momentum & kinetic energy are conserved 4) Neither momentum nor kinetic energy is conserved

4 20. If P is the pressure and V is the volume of a gas, then the dimensions of PV is same as those of 1) Force 2) work 3) pressure 4) power 21. A force of 10N acts on a body of mass 5kg so as to accelerate it from rest to a velocity of 5ms -1. The acceleration produced and the times taken respectively are, 1)2.0ms -2 & 2.5s 2)1.0 ms -2 & 1s 3)2.5 ms -2 & 2 s 4)0.5 ms -2 & 5s 22. A thick uniform rope of mass 6kg and length 3m is hanging vertically from a rigid support. The tension in the rope at a point 0.5m from the support will be (g=10ms -2 ) 1) 20N 2) 50N 3) 30N 4) 40N 23. The linear speed of the seconds hand of a wall clock is 1.05ms -1. The length of the hand is nearly: 1)1cm 2)10cm 3) 5cm 4) 60cm 24. A passenger is at a distance x from a bus when the bus begins to move with constant acceleration a. What is the minimum velocity with which the passenger should run towards the bus to catch it? 1) 2ax 2) ax 3) (2ax) 4) (ax) 25. When a stone is thrown up vertically with velocity v, it reaches a maximum height of h. If one wishes to triple the maximum height then the stone should be thrown with velocity 1) 3 v 2) 3v 3) 9v 4) 3/2v 26. An elastic spring has a length l 1 when it is stretched with a force of 2N and a length l 2 when stretched with a force of 3N.What will be length of the spring if it is stretched with a force of 5N? 1) l 1 + l 2 2) 1/2 (l 1 + l 2 ) 3) 3 l 2-2 l 1 4) 3 l 1-2 l 2

5 27. Three blocks are connected by mass less strings as shown on a frictionless table. They are pulled with a force T 3 = 40N. If m 1 =10kg, m 2 = 6 kg and m 3 =4kg, then tension T 2 will be T 1 T 2 T 3 = F m 1 m 2 m 3 1) 20N 2) 40N 3) 10N 4) 32N 28. Two billiard balls roll toward each other, both at a speed of 10 meters per second. They each have a mass of 350 grams. If the two balls are considered a system, then the total momentum of the system is: 1) 0 kg ms -1 2) 3.5 kg m s -1 3) 7 kg m s -1 4) 35 kg m s A truck carrying sand is moving on a smooth horizontal road (no friction) with a uniform speed 15ms -1. If a mass of 0.015kg of sand leaks in a time 10s from the bottom of the truck, the force needed to keep the truck moving at its uniform speed is 1) N 2) N 3) N 4) Zero 30. A car starts from rest and moves with constant acceleration. The ratio of the distance covered in the n th second and to that covered in n seconds is 1) [2/n 2-1/n] 2) [2/n 2 +1/n] 3) [2/n-1/n 2 ] 4) [2/n+1/n 2 ] 31. The displacement-time (s-t) graph of a body is shown in following figure. The accelerated path of the body is: 1) AB only 2) CD only 3) DE only. 4) AB and DE both.

6 32. The velocity-time graph of two bodies A and B are shown in figure, the ratio of their acceleration is: 1) 1: 3 2) 1:3 3) 3:1 4) 3: The velocity-time graph of a body is shown in figure, for the interval AD and DC the ratio of distance covered is: 1) 3:1 2) 1:3 3) 3:1 4) 3:2 34. A body of mass 4kg is accelerated upon by a constant force travels a distance of 5m in the first second and a distance of 2m in the third second. The force acting on the body is 1) 6N 2) 8N 3) 2N 4) 4N 35. The distance x covered in time t by a body having initial velocity u and having a constant acceleration a is given by x=ut+1/2at 2. This result follows from: 1) Newton s 1 st law. 2) Newton s 2 nd law 3) Newton s 3 rd law. 4) None of these laws 36. A drunkard is walking on a straight road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1m long and takes 1s.There is a pit on the road 11m away from the starting point. The drunkard will fall into the pit after, 1) 29s 2) 21s 3) 37s 4) 31s

7 37. A particle follows the path ABC where AB=BC= L. The displacement & the distance covered, for the particle is: B C A 1) L, L/2 2) 2L, L 3) L 2,2L 4) 2L 2, L 2 /2 38. A ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards right. Relative to its initial position with respect to the table, the ball. Force (1) Remains stationary if there is no friction between the paper and the ball (2) Moves to the left and starts rolling backwards, if there is friction between the paper and the ball (3) Moves forward, in the direction in which the paper is pulled. Here the correct statement/s is/ are.. 1) Both (1) & (2) 2) only (3) 3) only (1) 4) only (2) 39. The displacement time graph of a moving particle is given below. The instantaneous velocity of the particle is negative at the point: 1) A 2) B 3) C 4) D 40. The displacement x as a function of time t is given by, x = a sinwt. The acceleration of the particle is: 1) -asinwt 2) aw 2 sinwt 3) -aw 2 sinwt 4) -aw 2 coswt

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