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A stationary partical explodes into two ...

A stationary partical explodes into two partical of a masses `m_(1) and m_(2)` which move in opposite direction with velocities `v_(1) and v_(2)`. The ratio of their kinetic energies `E_(1)//E_(2)` is

A

`(m_(1))/(m_(2))`

B

`1`

C

`(m_(2))/(m_(1))`

D

`(m_(1)v_(2))/(m_(2)v_(1))`

Text Solution

Verified by Experts

The correct Answer is:
C

By the principle of conservation of linear momentum, `m_(1)u_(1) + m_(2)u_(2) = m_(1)v_(1) + m_(2) v_(2)`
` :. 3 xx 7 + 4 ( -5) = 3v_(1) + 4v_(2)`
`:. 21 - 20 = 3v_(1)+ 4v_(2)`
`:. 3v_(1) + 4v_(2) = 1 ` ....(1)
But `e = ( v_(2) - v_(1))/( u_(1)-u_(2)) = ( v_(2)-v_(1))/( 7( - 5)) = ( v_(2) - v_(1))/( 12)`
`:. (3)/(4) =( v_(2) - v_(1))/( 12)`
`:. v_(2) - v_(1) = 9` ....(2)
`:. 3v_(2)-3v_(1) = 9` ...(3)
Adding (1) and (3), we get
`7v_(2) = 28` `:. v _(2) = 4 m//s `
`:.` Speed of ball B after collision `= 4 m//s `
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