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Question

A string is wrapped several times round a solid cylinder and then the end of the string is held stationary while the cylinder is released from rest with an initial motion. The acceleration of the cylinder and tension in the string will be

A
2g3andmg3
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B
gandmg2
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C
g3andmg2
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D
g2andmg3
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Solution

The correct option is A 2g3andmg3
Let the mass of cylinder is m and radius of it is r.

so, moment of inertia of cylinder , I=12mr2

torque = moment of inertia * angular acceleration

force * displacement =12mr2×ar

we know, linear acceleration, a = r * angular acceleration

T×r=12mr×a

T=12ma ......(1)

now, net force = ma

weight - tension = ma

or, mg12ma=ma

or, mg=32ma

or, a=2g3

hence, tension in the string =12ma=mg3 and acceleration =2g3

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