Question

Two blocks, one of mass $A=1 \,kg$ and another $B=2\, kg$ are shown in figure. $A$ force of $5 \,N$ is applied on $A .$ Coefficient of friction between $A$ and $B$ is $0.2$ and that between $B$ and horizontal surface is zero. Find the time taken for the front face of $A$ to coincide with that of $B$.

• A. $ 2\sqrt{2}\,s $
• B. $ \sqrt{\frac{8}{3}}s $
• C. $ \sqrt{\frac{3}{8}}s $
• D. $ 2s $

Answer 1

Answer: (B)

The free body diagram of two blocks is shown in figure
$F-f=m a $
o $ F-\mu N=m a$

Or $5-0.2 \times 1 \times 10=1 \times a_{A}$
Or $a_{A}=3 m / s^{2}$
This is the acceleration of $A$ wrt $B$.
The time taken for the front surface of $A$ to coincide with that of $B$ is
$s=u t+\frac{1}{2} a_{A} t^{2} $
$4=0+\frac{1}{2} \times 3 \times t^{2}$
Or $t^{2}=\frac{8}{3}$
Or $t=\sqrt{\frac{8}{3}} \,s$