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Question

# A bullet of mass m is fired with the velocity of 50 ms−1 at an angle θ with the horizontal. At the highest point of its trajectory, it collides head-on with a bob of mass 4m connected with a massless string of length l=10/3 m and gets embedded with the bob. After the collision, the string moves to an angle of 120o. What is the angle θ

A
cos1(15)
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B
cos1(54)
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C
sin1(45)
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D
sin1(54)
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Solution

## The correct option is A cos−1(15)Given,mbullet=mmbob=4mAfter Collision,12(5)mv2=5mg×(l+lcos(60⊙)v2=g×3 lv= 10 ms1KE before collision = KE after collision12mv2i=125mv212m(50cos(θ))2=125m×1002500 cos2θ=500θ=cos−1(15)Hence, Option A is correct answer.

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