A `1 kg` solid sphere rolls without slipping on a rough horizontal surface under the influence of a `7 N` force. The force acts tangentially at the highest point of the sphere. Which of the following statements are correct? (`7 N` force acts towards right).

Options

A. The frictional force on the sphere acts towards right.
B. The value of the frictional force is `3 N`
C. The acceleration of the centre of the sphere is `9.8 m//s^(2)`
D. The acceleration of the centre of the sphere is `10 m//s^(2)`

Answer

A, B, D

Explanation

The point of contact between the sphere and the surface slips to the left. So the frictional force f acts towards the right.

If `a` is the linear acceleration of the centre of mass, then considering translational motion, we get
`7+f=1xxa` or `7+f=a`........i
Considering rotational motion about centre `C` we get
Net torque `=7R-fR=Ialpha`
`R[7-f]=[2/3xx1xxR^(2)]a/R`
`7-f=2/5a`..........ii
Adding eqn i and ii we get
`14=(7a)/5` or `a=10 m//s^(2)`
from eqn i `7+f=10` or `f=3N`