Question

A small block of mass $m$ is placed on a plank of mass $M$. The block is connected to plank with the help of a light string passing over a light smooth pulley as shown in figure. The co-efficient o static friction between the block and planks is $\mu$.
The co-efficient of friction between the plank and the horizontal surface is zero. What maximum horizontal force $F$ applied on the block of mass $m$ can make the block and plank not to slide relatively?

Answer 1

For this body to be in equilibrium,

$f=T$

$f=\mu mg$

So,

$F=T+f$

$F=2\mu mg$