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Q.

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

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a

mgRt(M+m)

b

2Mgt(M+2m)

c

2mgtR(M−2m)

d

2mgtR(M+2m)

answer is D.

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Detailed Solution

We know the tangential accelerationa=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+MSo, angular velocity of the cylinder, ω=vR=2mgtR(M+2m)
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