IIT-JEE 2011 · Paper 2 · Physics Q26

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PhysicsSingle correct+3 / -1Question 26 of 60

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity $V$ m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity $V$ of the bullet is

Ball on top of a post; a bullet arrives horizontally at V m/s. Dashed trajectories land at 20 m (ball) and 100 m (bullet) from the foot of the post.

250 m/s

250\sqrt2

m/s

400 m/s

500 m/s

Answer and worked solution

Official answer: D

Time of fall from 5 m: $t=\sqrt{2h/g}=1$ s, for both.

Velocities after impact. Ball: $20/1=20$ m/s. Bullet: $100/1=100$ m/s.

Momentum. $0.01V=0.2\times20+0.01\times100=5$ , so $V=500$ m/s.

(D)

Topics:Conservation of linear momentum Projectile motion

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IIT-JEE 2011 · Paper 2, Physics question 26