Question

Find the maximum value of M/m in the situation shown in figure so that the system remains at rest. Friction coefficient at both the contacts is $\mu$

• A. $\frac{\mu }{sin\theta -\mu cos\theta }$
• B. $\frac{2\mu }{sin\theta -\mu cos\theta }$
• C. $\frac{\mu }{sin\theta +\mu cos\theta }$
• D. $\frac{\mu }{cos\theta -\mu sin\theta }$

Answer 1

The correct option is C $\frac{\mu }{sin\theta +\mu cos\theta }$

$\begin{array}{c}\text{Correct option is}CC)\\ \text{If the system is at rest;}\\ \text{Fnet}=0\end{array}$

$\begin{array}{c}\mathrm{Mg}\sin \theta -\text{Friction}=0\\ \mathrm{Mg}\sin \theta -\mu (\mathrm{Mg}\cos \theta +mg)=0\end{array}$

$\begin{array}{c}M(g\sin \theta -\mu g\cos \theta )=\mu mg\\ M/m=\frac{u}{\sin \theta +\mu \cos \theta }\end{array}$