Question

In the figure, two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with co-efficient of friction $\mu$ and the mass $m$ is hanging vertically against a smooth vertical wall.(The pulley is frictionless)

Choose the correct statement(s):

• A. The system will accelerate for any value of $m$
• B. The system will accelerate only when $m>M$
• C. The system will accelerate only when $m>\mu M$
• D. Nothing can be said

Answer 1

Answer: (C)

The system will accelerate only when $m>\mu M$

The friction force on the mass $M$ due to rough surface is $f=\mu Mg$

In equilibrium,

For mass $m$,

$T=mg$ ,

for mass $M$,

$f=\mu Mg=T\Rightarrow$

$mg=\mu Mg\Rightarrow m=\mu M$
If $mg>\mu Mg$, then there would be an acceleration.
Thus, we get $m>\mu M$