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A ball of mass in moving with speed u un...

A ball of mass in moving with speed `u` undergoes a head-on elastic collision with a ball of mass `nm` initially at rest. The fraction of the incident energy transferred to the second ball is

A

`(n)/(1+n)`

B

`(n)/((1+n)^(2))`

C

`(2n)/((1+n)^(2))`

D

`(4n)/((1+n)^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
By conservation of momentum `m u = mv_(1) + nm v_(2)`
`u= v_(1) + nv_(2)` ….(i)
`v_(2) = v_(1) = u_(1) - u_(2)`
`4 v_(2) -v_(1) = u` …(ii)
(i) + (ii) `2u = (n + 1) v_(2)`
`v_(2) = (2u)/(n+1)`
Kinetic energy transferred `K_(t) = (1)/(2) (nm)v_(2)^(2), K_(t) = (2n m u^(2))/((n+1)^(2)), (K_(t))/(K_(i)) = (4n)/((n+1)^(2))`
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