Tiêu đề 07. SYSTEMS OF PARTICLES AND ROTATIONAL MOTION.pdf ✅

PAPER 1 (1.) Three particles of masses 1 kg,2 kg and 3 kg are situated at the coners of an equilateral triangle move at speed 1 1 6 ms ,3 ms − − and 1 2 ms− respectively. Each particle maintains a direction towards the particle at the next comer symmetrically. Find velocity of CM of the system at this instant : (1) 3 m / s (2) 5 m / s (3) 6 m / s (4) zero (2.) The coefficient of restitution e for a perfectly inelastic collision is : (1) 1 (2) 0 (3)  (4) -1 (3.) The centre of mass of a non-uniform rod of length L whose mass per unit length  varies as 2 kx L  = where k is a constant and x is the distance of any point on rod from its one end, is (from the same end) (1) 3/ 4 L (2) 1/ 4 L (3) K L/ (4) 3 K / L (4.) In a gravity free space, a man of mass M standing at a height h above the floor, throws a ball of mass m straight down with a speed u . When the ball reaches the floor, the distance of the man above the floor will be : (1) 1 m h M     +   (2) 2 m h M     −   (3) 2 h (4) A function of m,M,h and u (5.) An object of mass 3m splits into three equal fragments. Two fragments have velocities ˆ vj and ˆ vi The velocity of the third fragment is : (1) ˆ ˆ v j i     −   (2) ˆ ˆ v i j     −   (3) ˆ ˆ v i j   − +     (4) ˆ ˆ 2 v i j     −  
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(6.) A mass m is rest on an inclined plane of mass M which is further resting on a smooth horizontal plane. Now if the mass starts moving the position of C.M. of mass of system will : (1) remains unchanged (2) change along the horizontal (3) will move up in the vertical direction (4) will move down in the vertical direction and changes along the horizontal (7.) In a system of particles 8 kg mass is subjected to a force of 16N along +ve x -axis and another 8kg mass is subjected to a force of 8 N along +ve y axis. The magnitude of acceleration of centre of mass : (1) 5 2 m / s 2 (2) 5 2 m / s 3 (3) 3 2 m / s 5 (4) 2 2 m / s 5 (8.) The velocities of two particles A and B of same mass are ˆ V ai A = and ˆ V b j B = where a and b are constants. The acceleration of particleA is ˆ ˆ 2 4 ai b j     −   and acceleration of particle B is ˆ ˆ ai b j   −  ) (in 2 m / s ). The centre of mass of two particle will move in : (1) straight line (2) parabola (3) ellipse (4) circle (9.) When two bodies collide elastically, then : (1) Kinetic energy of the system alone is conserved (2) Only momentum is conserved (3) Both energy and momentum are conserved (4) Neither energy nor momentum is conserved (10.) A body of mass M collides against a wall with a velocity V and retraces its path with the same speed. The change in momentum is (take the initial direction of the velocity as positive) : (1) 2Mv (2) 1Mv (3) −2Mv (4) Zero (11.) A shell of mass m moving with velocity v suddenly breaks into 2 pieces. The part having mass m / 4 remains stationary. The velocity of the shell will be :
(1) (4 / 3) v (2) V (3) 2v (4) 3/ 4v (12.) A metal ball falls from a height of 32 metres on a steel plate. If the coefficient of restriction is 0.5 to what height will the ball rise after the second bounce : (1) 4 m (2) 8 m (3) 2 m (4) 16 m (13.) Consider a two particle system with particles having masses m1 and m2 . If the first particle is pushed towards the centre of mass through a distance d , by what distance should the second particle be moved, so as to keep the centre of mass at the same position : (1) 1 2 m d m       (2) 2 1 m d m       (3) 1 2 m 1 m d       (4) 2 1 m 1 m d       (14.) Which of the following statement is true? (1) Kinetic energy is conserved in all types of collisions. (2) By definition there is no difference between elastic and perfectly elastic collisions. (3) By definition there is no difference between inelastic and perfectly inelastic collisions. (4) After the collision, the relative displacement of the particles decreases with time. (15.) A ball moving with velocity 2 m / s collides head-on with another stationary ball of double the mass. If the coefficient of restitution is 0.5 , then their velocities (in m / s ) after collision will be :- (1) 0,1 (2) 1,1 (3) 1,0.5 (4) 0,2 (16.) A ball is dropped from height h on a plane. If the coefficient of restitution of the plane is e and if ball hits ground two times, the height upto which it reaches after two jumps, will be : (1) 4 eh (2) eh (3) 2eh (4) eh 2 (17.) Two bodies of masses 0.1 kg and 0.4 kg move towards each other with the velocities 1 m / s and 0.1 m / s respectively. After collision they stick together. In 10 sec the combined mass travels : (1) 120 m (2) 0.12 m (3) 12 m (4) 1.2 m (18.) Two masses of 0.25 kg each moves towards each other with speed 1 3 ms− and 1 1 ms− . Then they collide and stick together. Find the final velocity : (1) 1 0.5 ms− (2) 1 2 ms− (3) 1 1 ms− (4) 1 0.25 ms− (19.) Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R . If