Question

A small block of mass $1\text{kg}$ is placed over a plank of mass $2\text{kg}$. The length of the plank is $2\text{m}$. Coefficient of friction between the block and the plank is 0.5 and the ground over which plank is placed is smooth. A constant force $F=30\text{N}$ is applied on the plank in horizontal direction. The time after which the block will separate from the plank is $(g=10{\text{m/s}}^2)$ approximately

• A. $0.73\text{s}$
• B. $1.2\text{s}$
• C. $0.62\text{s}$
• D. $1.6\text{s}$

Answer 1

The correct option is A $0.73\text{s}$

Maximum frictional force between the block and the plank is
$f_{max}=\mu mg=\left(0.5\right)\left(1\right)\left(10\right)=5\text{N}$
The free body diagrams of the block and the plank are shown here

Acceleration of block $a_1=\frac{5}{1}=5{\text{m/s}}^2$
Acceleration of plank $a_2=\frac{30-5}{2}=\frac{25}{2}{\text{m/s}}^2$
$\therefore$ Relative acceleration of plank
$a=a_2-a_1$
or $a=\frac{25}{2}-5=7.5{\text{m/s}}^2$
$\therefore t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2\times 2}{7.5}}=0.73\text{s}$