A heavy steel ball of mass greater than $1\, kg$ moving with a speed of 2$m\,{\sec ^{ - 1}}$collides head on with a stationary ping-pong ball of mass less than $0.1\, gm$. The collision is elastic. After the collision the ping-pong ball moves approximately with speed ......... $m\,{\sec ^{ - 1}}$

  • A

    $2$

  • B

    $4$

  • C

    $2 \times {10^4}$

  • D

    $2 \times {10^3}$

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  • [AIEEE 2010]

In the figure shown, the two identical balls of mass $M$ and radius $R$ each, are placed in contact with each other on the frictionless horizontal surface. The third ball of mass $M$ and radius $R/2$, is coming down vertically and has a velocity $= v_0$ when it simultaneously hits the two balls and the smaller ball does not stop after collision, but continues to move downwards with $a$ speed $= v_0/2$, after the collision. Then, the speed of each bigger ball after collision is