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Two hail stones with radii in the ratio ...

Two hail stones with radii in the ratio of `1 : 2` fall from a great height through the atmosphere. Then the ratio of their momentum after they have attained terminal velocity is

A

`1:1`

B

`1:4`

C

`1:32`

D

`1:16`

Text Solution

Verified by Experts

The correct Answer is:
D
mass of sphere (m)`=4/3piR^3rho`
`:." "(m_2)/(m_1)=(4/3pi(R_2)^3)/(4/3pi(R_1)^3)=((R_2)/(R_1))^3=((2)/(1))^3=8`
`:." "(v_2)/(v_1)=((R_2)/(R_1))^2=((2)/(1))^2=4`
`:'` Momentum=Mass x Velocity
`:.` The ratio of their momenta
`((m_1)/(m_2))((v_1)/(V_2))=1/8xx1/4=1/(32)`
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