Question

A varying horizontal force $F=at$ acts on a block of mass m kept on a smooth horizontal surface. An identical block is kept on the first block. The coefficient of friction between the blocks is $\mu .$ The time after which the relative sliding between the blocks prevails is

• A. $\frac{2mg}{a}$
• B. $\frac{2\mu mg}{a}$
• C. $\frac{\mu mg}{a}$
• D. $2\mu mga$

Answer 1

The correct option is B $\frac{2\mu mg}{a}$

First, both the block will have same acceleration. As the force is applied on block below so the upper block will have a limiting acceleration which will be equal to the maximum frictional force / mass of upper block.

$a_{Umax}=\mu mg/m=\mu g$

When blocks going together:
Acceleration of both the block, $acc=F/(m+m)=at/2m$

Relative sliding between the blocks starts when common acceleration reaches the maximum possible acceleration of upper block:
$\frac{at}{2m}=\mu gt=\frac{2\mu mg}{a}$