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Two bodies having masses in the ratio 2:...

Two bodies having masses in the ratio 2:3 fall freely under gravity from heights 9:16. The ratio of their linear momenta on touching, the ground is

A

` 2:9`

B

`3:16`

C

`1:2`

D

`3:2`

Text Solution

Verified by Experts

The correct Answer is:
C
Momentum = mass `xx` velocity = p
`v^2 = u^2 + 2gh`
when `u = 0 , v^2 = 2gh :. v= sqrt(2gh)`
`p_1/p_2=(m_1v_1)/(m_2v_2)=(2/3)(sqrt(2gh_1))/(sqrt(2gh_2))`
`=2/3sqrt(h_1/h_2)=2/3xxsqrt(9/16)`
`=2/3 xx3/4 =1/2`
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