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In the following figure, a body of mass ...

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

`(mgR t)/((M + m))`

B

`(2Mg t)/((M+2m))`

C

`(2m g t)/(R(M-2m))`

D

`(2mg t)/(R(M + 2m))`

Text Solution

Verified by Experts

The correct Answer is:
D
We know the tangential acceleration `a= (g)/(1 + (I)/(mR^(2)))= (g)/(1+ (1//2MR^(2))/(mR^(2)))= (2mg)/(2m+ M)` [As `I= (1)/(2) MR^(2)` for cylinder]
After time t, linear velocity of mass m, `v= u + a t= 0 + (2mg t)/(2m+ M)`
So angular velocity of the cylinder `omega= (v)/(R )= (2 mg t)/(R(M + 2m))`
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