A solid sphere rools dwon without slipping on a smooth inclined plane of inclination `sin^(-1)(0.42)` if the acceleration due to gravity is `10ms^(-2)` the acceleration of the rolling sphere is

Options

A. `1 ms^(-2)`
B. `2 ms^(-2)`
C. `3ms^(-2)`
D. `4 ms^(-2)`

Answer

C

Explanation

Given inclination of incilined plane
`theta = sin^(-1) (0.42) rArr sin theta = 0.42 `
Acceleration due to gravity
`g= 10 m//s^(2)`
Acceleration of rolling solid sphere on the inclined plane without slipping is given by
`a= (g sin theta)/(1+(1)/(MR^(2)))`
Where I = moment of ineria
M = mass of sphere
R = radius of sphere
But `l = (2)/(5) mr^(2+)`
`:. , a= (g sin theta)/(1+ (2)/(5) MR^(2))/(MR^(@)) = (5)/(7) g sin theta`
`= (5)/(7) xx 10 xx 0.42 = 3 m//s^(2)`