Numerical Problems : Collision , COM & Impulse

LEVEL – I

Q:1. Two particles A and B of which lighter particle has mass m, are released from infinity. They move towards each other under their mutual force of attraction. If their speeds are v and 2 v respectively find the K.E. of the system.

Ans: $\displaystyle \frac{3}{2}m v^2$

Q:2. A bullet of mass 0.01 kg travelling at a speed of 500 m/s strikes a block of mass 2 kg which is suspended by a string of length 5 m. The centre of gravity of the block is found to rise a vertical distance of 0.2 m. What is the speed of the bullet after it emerges from the block?

Ans : 100 m/s

Q:3. A body of mass 1 kg initially at rest, explodes and breaks into three fragments of masses in the ratio 1 : 1 : 3. The two pieces of equal mass fly off perpendicular to each other with a speed of 15 m/s each. What is the velocity of the heavier fragment?

Ans: 20/3 m/s

Q:4. Steel ball of mass 0.5 kg is fastened to a cord 20 cm long and fixed at the far end and is released when the cord is horizontal. At the bottom of its path the ball strikes a 2.5 kg steel block initially at rest on a frictionless surface. The collision is elastic. Find the speed of the block, just after the collision.

Ans: 5 √2 m/s

Q:5. A particle loses 25% of its energy during collision with another identical particle at rest. Find the coefficient of restitution.

Ans : e = 1/√2

Q:6. A body of mass 3 kg collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. What is the mass of the target body?

Ans: 1 kg

Q:7. An automatic gun fires 600 bullets a minute. The mass of each bullet is 4 gm and its initial velocity is 500 m/s. Find the mean impact force experienced by the gun.

Ans: 20 N

Q:8. A skater of mass m standing on ice throws a stone of mass M with a velocity of v m/s in a horizontal direction. Find the distance over which the skater will move back if the coefficient of friction between the skaters and the ice is μ .

Ans: $\displaystyle (\frac{Mv}{m})^2/2\mu g$

Q:9. A steel ball with a mass of m = 20 g falls from a height of h1 = 1 m onto a steel plate and rebounds to a height of h2 = 81 cm. Find: the impulse of the force received by the plate during the impact.

Ans: $\displaystyle m(\sqrt{2gh_1} + \sqrt{2gh_2})$

Q:10. A ball collides with an inclined plane of inclination θ after falling through a distance h. If it moves horizontally just after the impact, find the coefficient of restitution.

Ans: $\displaystyle e = tan\theta$

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