Question

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 $m>M$
• C. The system will accelerate only when $m>\mu M$
• D. Nothing can be said

Answer 1

Answer: (C)

$N=Mg$
$f_{\max }=\mu Mg$
Applying Newton's II law
for $m$,
$mg-T=ma$
for $M$,
$T-F=Ma$
for $a=0$,
$T=mg=f$
also $f\le \mu Mg$
$\therefore m\le \mu M$