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A uranium 238 nucleus, originally at res...

A uranium 238 nucleus, originally at rest, emits and `alpha` particle. The `alpha` particle travels with a speed of v m/s. What is the recoil speed of the residual necleus?

A

`v/4m//s`

B

`-(2v)/117m//s`

C

`-(117v)/2m//s`

D

`(4v)/238m//s`

Text Solution

Verified by Experts

The correct Answer is:
B
The velocity of the body after 5s is given by
`v = u - g t =100- 10 xx 5 = 50 m//s`
`:. ` Linear momentum of the body before explosion
`:. Mv = 1 xx 50 = 10`
Part A of mass 0.4 kg has a velocity of `25 m//s `. Let v' be the velocity of the part B of mass 0.6kg .
`50= 0.4 xx ( - 25) + 0.6 xx v' ` `:. 50 = - 10 xx 0.6 v'`
`:. 60 = 0.6v'` `:. v' = ( 60)/( 0.6) = 100 m //s `
`:.` Velocity of B = `100 m//s` upwards
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