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A round uniform body of radius R, mass M...

A round uniform body of radius `R`, mass `M` and moment of inertia 'I' rolls down (without slipping) and inclined plane making an angle `theta` with the horizontal. Then its acceleration is.

A

`(g sin theta)/(1-MR^(2)//I)`

B

`(g sin theta)/(1 +I//MR^(2))`

C

`(g sin theta)/(1 +MR^(2)//I)`

D

`(g sin theta)/(1-I//MR^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
`mg sin theta - f = ma_(CM)`…(i)
`f.R = I alpha`…(ii)

`a_(CM) = R alpha` …(iii)
On solving (i),(ii) & (iii)
`a_(CM) = (g sin theta)/(1 + (I)/(MR^(2)))`.
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