A solid sphere rolls without slipping on an inclined plane of angle `theta`. Find its linear acceleration in the direction parallel to the surface of the inclined plane.

Options

A. `(5)/(7)gsintheta`
B. `(7)/(5)gsintheta`
C. `(3)/(5)gsintheta`
D. `(1)/(2)gsintheta`

Answer

A

Explanation

Acceleration of body parallel to the plane is
`a=(gsintheta)/(1+(k^(2))/(R^(2)))`
but for sphere `k^(2)=(2)/(5)R^(2)`
`therefore a=(gsintheta)/(1+(2R^(2))/(5R^(2)))`
`therefore a=(5gsintheta)/(7)`