Question

In the figure shown below, the block on the frictionless surface is having acceleration $a$ towards left and the other block is having acceleration $a^{\prime }$. Find the relation between the accelerations of the two blocks.

• A. $a=a^{\prime }$
• B. $a=2a^{\prime }$
• C. $a=\frac{a^{\prime }}{2}$
• D. $a=\frac{3}{2}{a}^{\prime }$

Answer 1

The correct option is A $a=a^{\prime }$


Let $l_1,l_2\&l_3$ be the intercepts of the same string.
$\therefore l_1+l_2+l_3=\text{constant}$ --- (i)
Also $l_2$ is fixed as the two pulleys 1 & 2 are fixed
$\therefore l_2=\text{constant}$ --- (ii)
Differentiating (i) w.r.t. time
$v_1+v_2-v_3=0$ --- (iii) ($\because$ $l_3$ is decreasing)
Now differentiating (ii) w.r.t. time
$v_2=0$ --- (iv)

Putting (iv) in (iii)
$v_1-v_3=0$
Now differentiating again w.r.t. time
$\Rightarrow a_1-a_3=0$
$\Rightarrow a_1=a_3$
$\Rightarrow a=a^{\prime }$