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 pece moves with speed `v//2`
C. One of the pieces moves with speed `v//2`, the othher 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)sin theta -mv_(3)sin theta `
`rArr v_(2)=v_(3)`
Along `x-` axis
`mv=0+mv_(2)cos theta +mv_(3)cos theta `
`mv=2mv_(2)cos theta`
`v_(2)=(v)/(2)(1)/(cos theta )` so `v_(2)=v_(3)lt(v)/(2):' cos theta lt1`