Question

Two particles of mass m, constrained to move along the circumference of a smooth circular hoop of equal mass m, are initially located at opposite ends of a diameter and given equal velocities $v_0$ shown in the figure. The entire arrangement is located in gravity free space. Their velocity just before collision is?

• A. $\frac{1}{\sqrt{3}}{v}_0$
• B. $\frac{\sqrt{3}}{2}{v}_0$
• C. $\frac{2}{\sqrt{3}}{v}_0$
• D. $\frac{\sqrt{7}}{3}{v}_0$

Answer 1

The correct option is D $\frac{\sqrt{7}}{3}{v}_0$

consider p is the particle velocity

h hoop velocity at the impact

conservation of momentum at the impact

$2mv0=3mvh$

conservation of energy

$2\times 12mv20=12mv2h+2\times 12mv2p$

solve we obtain

$vp=\sqrt{7}/3v0$