Title 05. LAWS OF MOTION.pdf ✅

PAPER 1 (1.) A particle moves in the xy -plane under the action of a force F such that the components of its linear momentum p at any time t are 2cos , 2 x y p t p = = sint . The angle between F and p is : (1) 90 (2) 0 (3) 180 (4) 30 (2.) A shell of mass 200g is fired by a gun of mass 100 kg . If the muzzle speed of the shell is 1 80 ms− , then the recoil speed of the gun is : (1) 1 16 cm s− (2) 1 8 cm s− (3) 1 8 ms− (4) 1 16 ms− (3.) A large cubical shaped block of mass M rests on a fixed horizontal surface. Two blocks of mass m1 and m2 are connected by a light inextensible string passing over a light pulley as shown. Neglect friction everywhere. Then the constant horizontal force of magnitude F that should be applied M so that m1 and m2 do not move relative to M is : (1) ( ) 2 1 2 1 m F m m M g m = + + (2) ( ) 1 1 2 2 m F m m M g m = + + (3) ( ) 1 1 2 m F m M g m = + (4) ( ) 2 1 1 m F m M g m = + (4.) Five forces 1 2 3 4 F F F F , , , and F5 are acting on a particle of mass 2.0 kg so that it is moving with 4 2 m/s in east direction. If F1 force is removed, then the acceleration becomes 2 7 m / s in north, then the acceleration of the block if only F1 is acting will be : (1) 2 16 m / s (2) 2 65 ms (3) 2 260 ms (4) 2 33 ms (5.) A body of mass 0.4 kg starting at origin at t = 0 with a speed of 1 10 ms− in the positive x -axis direction is subjected to a constant F = 8N towards negative x -axis. The position of the body after 25 s is :
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(1) −6000m (2) −8000m (3) +4000 m (4) +7000m (6.) In the arrangement shown in figure the ends P and Q of an non-stretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed: (1) 2 cos U  (2) Ucos (3) 2 cos U  (4) cos U  (7.) Three blocks 1,2 and 3 are arranged as shown in the figure. The velocities of the blocks 1 2 v v, and 3 v are shown in the figure. What is the relationship between 1 2 v v, and 3 v : (1) 1 2 3 2v v v + = (2) 1 2 3 v v v + = (3) 1 2 3 v v v + = 2 (4) 1 2 3 2 2 v v v + = (8.) In the following arrangement the system is initially at rest. The 5 kg block is now released. Assuming the pulley and string to be massless and smooth, the acceleration of block ' C ' will be :
(1) zero (2) 2 2.5 m / s (3) 10 2 m / s 7 (4) 5 2 m / s 7 (9.) In the figure acceleration of A is 2 1 m / s upwards, acceleration of B is 2 7 m / s upwards and acceleration of C is 2 2 m / s upwards. The acceleration of D will be : (1) 2 7 m / s downwards (2) 2 2 m / s downwards (3) 2 10 m / s downwards (4) 2 8 m / s downwards. (10.) Two blocks A and B of masses 2m and m , respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitude of acceleration of A and B immediately after the string is cut, are respectively: (1) , 2 g g (2) , 2 g g (3) g,g