Q.

A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, travelling with a velocity ν 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 ν of the bullet is

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a

250 m/s

b

2502m/s

c

400 m/s

d

500 m/s

answer is D.

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Detailed Solution

Time taken by the bullet and ball to strike the ground ist=2hg=2.510=1sLet ν1 and ν2 be the velocities of ball and bullet aftercollision. Then applying,x = νtWe have, 20=v1⋅1 or v1=20m/s100=v2.1 or v2=100m/sNow, from conservation of linear momentum before and after collision we have,0.01v=(0.2.20)+(0.01.100)On solving, we getv = 500 m / s.
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A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, travelling with a velocity ν 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 ν of the bullet is