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

Options

A. `(gsintheta)/(1-(MR^(2))/(I))`
B. `(gsintheta)/(1+(I)/(MR^(2)))`
C. `(gsintheta)/(1+(MR^(2))/(I))`
D. `(gsintheta)/(1-(I)/(MR^(2)))`

Answer

B

Explanation

Acceleration of body rolling from incline plane,
`a=(gsintheta)/(1+(K^(2))/(R^(2)))`
but for radius of gyration K
`I=MK^(2)`
`therefore K^(2)=(I)/(M)`
`therefore a=(gsintheta)/(1+(I)/(MR^(2)))`