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Question:

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. Then the acceleration of the body is :

2Mg/(2m+M)

2mg/(2m+M)

2Mg/(2M+m)

2mg/(2M+m)

Solution:

T=Iα
F.R=Iα
mgR=(MR²/2 + mR²)α
2mgR=(2m+M)R²α/R
a=2mg/(2m+M)