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 \[N=Mg+T=\left( M+m \right)g\] |
\[T\le m\left( M+m \right)g\] |
\[mg\le \mu \left( M+m \right)g\] |
\[\frac{m}{M}\le \frac{\mu }{\left( 1-\mu \right)}\] |
\[\frac{m}{M}\le \frac{0.75}{\left( 1-0.75 \right)}\Rightarrow \frac{m}{M}\le 3\] |
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