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4 identical balls of radius R and mass m...

`4` identical balls of radius `R` and mass `m` are lying a gravity free space. The balls are in contact and there centres are forming vertices of a square of side `2R` in horizontal plane. One identical ball travelling vertically with a speed `v` hits the four balls symmetrically. The collision is perfectly elastic. The centre of the `4` stationery ball are at (`R`, `R`, `0`), (`R`, `-R`, `0`) and (`-R`, `-R`,`0`) initially.
The speed of ball `1` after collision is :

A

`(sqrt(2))/(3)v`

B

`(v)/(sqrt(2))`

C

`(6)/(11)sqrt((2)/(3))`

D

none of these

Text Solution

Verified by Experts

`mv=(4mv_(1))/(sqrt(2))+mv_(2)`……(`1`)
`1=(v_(1)=(v_(2))/(sqrt(2)))/(v//sqrt(2))`.....(`2`)
`v_(1)=(sqrt(2)v)/(3)`
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