Question

A solid sphere is placed on an inclined plane. The friction coefficient between the plane and the sphere is $\mu$.
For which of the following cases will the friction acting on the sphere be dissipative?

• A. $\mu =0.2,\theta ={30}^{\circ }$
• B. $\mu =0.25,\theta ={45}^{\circ }$
  
• C. $\mu =0.2,\theta ={37}^{\circ }$
  
• D. $\mu =0.6,\theta ={53}^{\circ }$

Answer 1

The correct option is C $\mu =0.2,\theta ={37}^{\circ }$


For pure rolling, $\mu >\frac{tan\theta }{(1+\frac{R^2}{K^2})}$

For sphere $\mu >\frac{2}{7}tan\theta$

For $\theta ={30}^{\circ },{\mu }_{min}$ = 0.165, given $\mu =0.2>0.165$

For $\theta ={45}^{\circ },{\mu }_{min}$ = 0.202, given $\mu =0.25>0.202$

For $\theta ={37}^{\circ },{\mu }_{min}$ = 0.21, given $\mu =0.2<0.21$

For $\theta ={53}^{\circ },{\mu }_{min}$ = 0.38, given $\mu =0.6>0.38$