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In the following figure, a body of mass 'm' is tied at one end of a light string and this string is wrapped around the solid cylinder of mass 'M' and radius 'R'. At the moment, t = 0 the system starts moving. If the friction is negligible, angular velocity at time, t would be

A
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B
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C
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D
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Solution

The correct option is B
We know the tangential acceleration a=g1+ImR2=g1+1/2MR2mR2=2mg2m+M [As I=12MR2 for cylinder]
After time t, linear velocity of mass m,v=u+at=0+2mgt2m+M
So angular velocity of the cylinder ω=vR=2mgtR(M+2m).

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