Question

Block $A$ of mass $m$ rests on the plank $B$ of mass $3m$ which is free to slide on a frictionless horizontal surface. The coefficient of friction between the block and plank is $0.2$. If a horizontal force of magnitude $2mg$ is applied to the plank $B$, the acceleration of $A$ relative to the plank and relative to the ground respectively, are

Answer 1

The weight of block A is $mg$.

The acceleration of block A relative to ground is given as,

$ma=0.2\times W$

$ma=0.2\times mg$

$a=0.2g$

The acceleration of plank B is given as,

$m{a}_1=\left(2-0.2\right)\times W$

$m{a}_1=1.8\times m\frac{g}{3}$

$a_1=0.6g$

The acceleration of block A relative to plank B is given as,

$a_2=\left(0.2-0.6\right)g$

$=-0.4g$

Thus, acceleration of block A relative to the plank B is $-0.4g$ and relative to the ground is $0.6g$.