A particle of mass `m` is moving along the `x`-axis with speed v when It collides with a particle of mass `2m` initially at rest. After the collision, the first particle has come to rest and the second particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the two places? `(thetagt0)`

Options

A. each piece moves with speed `v`.
B. each piece moves with speed `v//2`.
C. one of the pieces moves with speed `v//2`, the other moves with speed greater than `v//2`.
D. each piece moves with speed greater than `v//2`.

Answer

D

Explanation

After collision by momentum conservation

Along `y`-axis:
`0=0+mv_(2)sintheta-mv_(3)sinthetaimpliesv_(2)=v_(3)`
along `x`-axis:
`mv=0+mv_(2)costheta+mv_(3)costheta`
`mv=2mv_(2)costheta`
`v_(2)=v/2 1/(costheta)` so so `v_(2)=v_(3)gtv/2:'costhetalt1`