Question

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

• A. downwards and $\mu mg\cos \theta$
• B. downwards and $\frac{2mg\sin \theta }{7}$
• C. upwards and $\mu mg\cos \theta$
• D. upwards and $\frac{2mg\sin \theta }{7}$

Answer 1

The correct option is D upwards and $\frac{2mg\sin \theta }{7}$

Acceleration of a body rolling (pure) down the inclined plane , $a=\frac{gsin\theta }{1+K}$

For solid sphere $K=\frac{2}{5}$

Let assume friction force to act upwards.

Equation of motion, $ma=mgsin\theta -f$

$\frac{5}{7}mgsin\theta =mgsin\theta -f$

$⟹f=\frac{2}{7}mgsin\theta$

As $f$ comes out to be positive thus our assumption is correct.