The least coefficient of friction for an inclined plane inclined at angle $\alpha$ with horizontal in order…
The least coefficient of friction for an inclined plane inclined at angle $\alpha$ with horizontal in order that a solid cylinder will roll down without slipping is
\(\frac{2}{3} \tan \alpha\)
\(\frac{2}{7} \tan \alpha\)
\(\frac{1}{3} \tan \alpha\)
\(\frac{4}{3} \tan \alpha\)
Solution
\(\mu_{\min }=\frac{\tan \alpha}{1+\frac{\mathrm{mR}^2}{\mathrm{I}}}=\frac{\tan \alpha}{1+2}=\frac{1}{3} \tan \alpha\) as \(I=\frac{1}{2} \mathrm{mR}^2\)
.