A sphere has to purely roll upwards. At an instant when the velocity of sphere is `v,` frictional force acting on it is

Options

A. a)downwards and `mumgcostheta`
B. b)downwards and `(2mgsintheta)/7`
C. c)upward and `mumgcostheta`
D. d)upwards and `(2mgsintheta)/7`

Answer

D

Explanation

In case of rolling in the inclined plane, friction is static and acts in the upward direction and is given by
`f=(mgsintheta)/(1+(R^(2))/(k^(2)))`………..i
Form sphere `k^(2)=2/5R^(2)` ……….ii
Form eqn i andii `f=2/7 mgsintheta` (upwards)