Question

Two particles $A$ and $B$ each of mass $m$ are attached by a light inextensible string of length $2l$ . The whole system lies on a smooth horizontal table with $B$ initially at a distance $l$ from $A$ . The particle at the end $B$ is projected across the table with speed $u$ perpendicular to $AB$ . The velocity of the ball $A$ just after the string is taut, is

• A. $\frac{u\sqrt{3}}{4}$
• B. $u\sqrt{3}$
• C. $\frac{u\sqrt{3}}{2}$
• D. $\frac{u}{2}$

Answer 1

Answer: (A)

When the string jerk tight both particles begin to move with velocity components $v$ in the direction $AB$ . Using conservation of momentum in the direction $AB$
$mucos30^{\circ }=mv+mv$
or $v=\frac{u\sqrt{3}}{4}$
Hence, the velocity of ball $A$ just after the jerk is $\frac{u\sqrt{3}}{4}$