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Two bodies with kinetic energies in the ...

Two bodies with kinetic energies in the ratio 4:1 are moving with equal linear momentum. The ratio of their masses is

A

`1:2`

B

`1:4`

C

`2:1`

D

`16:1`

Text Solution

Verified by Experts

The correct Answer is:
B
`A//q, m_(1)v_(1)= m_(2) v_(2) rArr (v_(1))/(v_(2))= (m_(1))/(m_(2))`
Now, `((1)/(2) m_(1)v_(1^(2)))/((1)/(2) m_(2) v_(2)^(2))= (4)/(1)`
`rArr (m_(1))/(m_(2)) ((v_(1))/(v_(2)))^(2)= 4//1, rArr (m_(1))/(m_(2)) (m_(2)^(2))/(m_(1)^(2)) = (4)/(1)`
`rArr (m_(2))/(m_(1))= (4)/(1)`
`rArr m_(1): m_(2)= 1:4`
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