question_answer

Two blocks (m and M) are arranged as shown in Fig. 21. If there is friction between ground and M only and other surfaces are frictionless. The coefficient of friction between ground and M is \[\mu =0.75\] . The maximum ratio of m and M (m/M) so that the system remains at rest is

A) \[1/4\]              

B) 3

C) \[1/3\]              

D) None of these

Correct Answer: B

Solution :

As sphere is at rest,

\[T=mg\]

\[f=T\]

and       \[f\le \mu \,N\]

Here \[N=Mg+T=\left( M+m \right)g\]

\[T\le m\left( M+m \right)g\]

\[mg\le \mu \left( M+m \right)g\]

\[\frac{m}{M}\le \frac{\mu }{\left( 1-\mu  \right)}\]

\[\frac{m}{M}\le \frac{0.75}{\left( 1-0.75 \right)}\Rightarrow \frac{m}{M}\le 3\]