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Q.

A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming the pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

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a

23g

b

32g

c

g

d

g3

answer is B.

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Detailed Solution

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For the mass, m:

 mg-T=ma .......(1)

Question Image

The pulley experiences a torque. If α is its angular acceleration, then 

τ=TR=Iα 

Now, I=12 MR2 and α=aR,  therefore,

TR=12MR2aR⇒ T=12 Ma 

substituting in Eq.(1) ,

mg-12ma=ma ⇒ a=2g3

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