Question

A hollow spherical ball is given an initial push up an incline of inclination angle $\alpha$. The ball rolls purely. The coefficient of static friction between the ball and incline $=\mu$. During its upwards journey

• A. friction acts up along the incline
• B. ${\mu }_{min}=\left(2\tan \alpha \right)/5$
• C. friction acts down along the incline
• D. ${\mu }_{min}=\left(2\tan \alpha \right)/7$

Answer 1

Answer: (A), (B)

The correct options are
A friction acts up along the incline
B ${\mu }_{min}=\left(2\tan \alpha \right)/5$

$mg\sin \theta R=\frac{5}{3}m{r}^2\alpha f+mg\sin \theta =ma$

Here f is assumed to act down the plane but f comes out to be negative.

So f acts upwards.

$fR=I\alpha mg\sin \theta -f=maf=\mu mg\cos \theta$

Solve to get the expression for coefficient of friction