Question

Block $B$ moves to the right with a constant velocity $v_0.$ Assuming the pulleys and the surface to be smooth and the string to be inextensible, the velocity of block $A$ relative to block $B$ is

• A. $\frac{v_0}{2},$ towards left
• B. $\frac{v_0}{2},$ towards right
• C. $\frac{3v_0}{2},$ towards left
• D. $\frac{3v_0}{2},$ towards right

Answer 1

The correct option is B $\frac{v_0}{2},$ towards right

Given condition of the system is shown below

Let the velocity of block $A$ be $v_2$
Considering the points from $1$ to $6$ we have
$0+v_0+v_0+v_2+v_2+v_0=0$
$\Rightarrow v_2=-\frac{3v_0}{2}$
So, the velocity of block $A$ will be $\frac{3v_0}{2}$ towards right
Thus, velocity of block $A$ relative to block $B$ is given as
$v_{AB}=v_A-v_B=\frac{3v_0}{2}-v_0=\frac{v_0}{2}$, towards right