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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

`1:64 `

B

`1:32`

C

`1:16`

D

`1:8`

Text Solution

Verified by Experts

The correct Answer is:
B
Terminal velocity `prop "(radius)"^2` , for a drop / sphere
` therefore v_1/v_2 = (r_1/r_2)^2 = (1/2)^2 = 1/4`
As mass = volume x density = `4/3 pi r^3.rho " or " m prop r^3`
`m_1/m_2 = (r_1/^3)/(r_2^3) = (r_1/r_2)^2 = (1/2)^3 = 1/8`
Ratio of momenta ` = (m_1v_1)/(m_2v_2) = 1/8 xx 1/4 = 1/32`
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