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 $f \leq \mu\, Mg$
$\therefore m \leq \mu \,M$