Question

A small block of mass $1kg$ is placed over a plank of mass $2kg$. The length of the plank is $2m$. 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 $F=30N$ is applied on the plank in horizontal direction. The time after which the block will separate from the plank is $(g=10m/s^2)$

• A. $0.73s$
• B. $1.2s$
• C. $0.62s$
• D. $1.6s$

Answer 1

The correct option is A $0.73s$

The free body diagrams of the block and the plank are shown here

From the FBD of $1kg$ block, we have
$N_1=1g=10\text{N}$
Maximum frictional force between the block and the plank is
$f_{max}=\mu N_1=0.5\times 10=5\text{N}$

Since $f_{max}<30N$, the plank will move with acceleration
$a_p=\frac{30-f}{m_p}=\frac{30-5}{2}=\frac{25}{2}m/s^2$

Acceleration of the block is given by
$a_b=\frac{f_{max}}{m_b}=\frac{5}{1}=5m/s^2$

$\therefore$ Relative accelearation of plank w.r.t block is
$a_{pb}=a_p-a_b=\frac{25}{2}-5=7.5m/s^2$

From equation of motion, time taken for the plank and block to separate
$t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2\times 2}{7.5}}=0.73s$