Question

When a rolling body moves along an inclined plane, frictional force acts at the point of contact so as to either prevent the relative sliding or oppose the relative sliding. In the case of a rolling body when projected up or down along the inclined plane or spun with some angular speed and kept on the inclined plane, kinetic force of friction comes into play. If we release the body from rest and the angle of inclination $\theta \left({\theta }_0\right)$ where ${\theta }_0$ = minimum angle for which pure rolling can be established, static force of friction comes into play. For instance, let the body (a solid uniform m sphere of mass m, say) be spun with ${\omega }_0\downarrow$ and kept on the inclined plane.
The minimum coefficient of friction for which the sphere will have pure rolling after some time for $\theta ={45}^{\circ }$ is :

• A. $\frac{2}{7}$
• B. $\frac{1}{7}$
• C. $\frac{2}{5}$
• D. none of these

Answer 1

Answer: (A)

$\frac{2}{7}$

$\begin{array}{c}\text{Given}\theta =45\\ \begin{array}{c}\mu =\frac{2}{7}\tan \theta \text{for sphere in pure rolling}\\ \mu =\frac{2}{7}\end{array}\\ \text{Hence option}A\text{is correct}\end{array}$