A solid sphere is rolling down in the inclined plane, from rest without slipping. The angle of inclination with horizontal is `30^(@)`. The linear acceleration of the sphere is___ (Assume `g=10ms^(-2)`)

Options

A. (a) `28 ms^(-2)`
B. (b) `3.9ms^(-2)`
C. (c) `(25)/(7) ms^(-2)`
D. (d) `(1)/(20)ms^(-2)`

Answer

C

Explanation

We know that `a=(g sin theta)/(1+(k^(2))/(R^(2)))=(g sin 30^(@))/(1+(2)/(5))`
`:.(k^(2))/(R^(2))` for solid sphere `=(2)/(5)`
`a=(10xx(1)/(2))/((7)/(5))=(25)/(7)=3.6 ms^(-2)`