An ideal spring is wrapped around a cylinder that is free to rotate with negligi

Question

An ideal spring is wrapped around a cylinder that is free to rotate with negligible friction about a stationary horizontal axis. The free end of the string is attached to a massive object. When the object is released from rest at a heigh h above the floor gravity pulls it downward causing the string to unwind and the cylinder to turn. The time it takes for the object to reach the floor:

A. Is independent of the moment of inertia of the cylinder

B. Get longer if the cylinder is replace with one having larger moment of inertia

C. Gets shorter if the cylinder is replaced with one having larger moment of inertia

Explanation / Answer

answer is C

explanation :

torque on the cylinder = the force exerted by the string on the cylinder

force exerted by string on cylinder = force of gravity of mass attached to the string = m.g (mass x accelration due to gravity)

=> torque = m . g

and torque = (moment of inertia).(angular acceleration )

=> (moment of inertia).(angular acceleration ) = m . g

=> angular acceleration = m . g / (moment of inertia)

=> angular accelaration will dicrease on increasing moment of inertia

and as angular acceleration dicrease the time required by block to reach ground also dicrease !!

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