Q.

A circular disc of mass m and radius R rests flat on a horizontal frictionless surface. A bullet, also of mass m and moving with a velocity v, strikes the disc and gets embedded in it. If the disc is free to rotate about a fixed axis passing through its center then the angular velocity with which the system rotates after the bullet strikes the hoop is

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answer is 3.

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Detailed Solution

Conservation of angular momentum about the axis of rotationmvR=Itotalω                     =mR2+12mR2ω=3mR22ω∴ω=2v3R
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A circular disc of mass m and radius R rests flat on a horizontal frictionless surface. A bullet, also of mass m and moving with a velocity v, strikes the disc and gets embedded in it. If the disc is free to rotate about a fixed axis passing through its center then the angular velocity with which the system rotates after the bullet strikes the hoop is