In figure, two blocks M and m are tied together with an inextensible and light string. mass M is pla

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4-2.Friction

hard

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 $(s)$

AThe system will accelerate for any value of $m$

BThe system will accelerate only when $m > M$

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

DNothing can be said

Solution

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 $m>\mu M$

Standard 11

Physics