Q.

A solid cube ABCD of side a and mass M is placed on a rough horizontal surface. A bullet of mass m and speed v is shot at the top of the cube so that cube rotates aboutpoint D. The bullet sticks to the cube, m << M. Find the angular velocity of the cube.

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a

6mv4Ma

b

3Mv2ma

c

2Mv3ma

d

2mv3Ma

answer is A.

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Detailed Solution

Angular momentum about point D is conserved.mva=IDω But ID=46Ma2. So, ω=6mv4Ma
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A solid cube ABCD of side a and mass M is placed on a rough horizontal surface. A bullet of mass m and speed v is shot at the top of the cube so that cube rotates aboutpoint D. The bullet sticks to the cube, m << M. Find the angular velocity of the cube.