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IAT IISER2021PhysicsRotational Motion

A door of mass M and width L is hinged at one end and rotates about a vertical axis without friction. A bullet of mass m(m M) fired perpendicularly to the door at a speed v gets embedded in it at a distance x from its axis of rotation. Assuming the door was stationary initially, how does the resultant angular speed of the door vary as a function of x ?

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