Question

Two identical small balls, each of mass $m$, are connected by a massless and inextensible string of length $l$ and placed on a smooth horizontal xy plane. An external agent starts pulling the string from its mid-point along y-axis with velocity $v_0$ as shown in figure. When the separation between the two balls reduces to $\frac{l}{2}$, then the speed of each ball will be:

• A. $2v_0$
• B. $v_0$
• C. $\frac{v_0}{2}$
• D. None of the above.

Answer 1

Answer: (B)

$v_0$

Using conservation of angular momentum about the midpoint, we can find the velocity of each ball relative to the midpoint, i.e., $v^{\prime }=v_0$.
Resultant velocity of ball $=$ velocity of midpoint + velocity of ball w.r.t. midpoint
or $v=\sqrt{v_0^2+v_0^2+2v_0^{2}cos{120}^o}=v_0$