In figure, two blocks M and m are tied together with an inextensi… - Vidyadip

MCQ

In 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 coefficient 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 $m > M$
✓
The system will accelerate only when $m > \mu M$
D
Nothing can be said

✓

Answer

Correct option: C.

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

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

In equilibrium,

For mass $m$

$T=m g$

for mass $M$

$f=\mu M g=T \Rightarrow$

$m g=\mu M g \Rightarrow m=\mu M$

If $m g>\mu M g,$ then there would be an acceleration.

Thus, we get $m>\mu M$

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