Two spherical rain drops with radii in the ratio `1: 2` fall from a great height through the atmosphere. The ratio of their momenta after they have attained terminal velocity is

Options

A. `1:8`
B. `2:1`
C. `1:32`
D. `1:2`

Answer

C

Explanation

Given `r_1 : r_2 = 1:2`
We know that
`v prop r^3 and m prop r^3`
`(v_1)/(v_2) = ((r_1)/(r_2))^3 and (m_1)/( m_2) = ((r_1)/(r_2))^3`
We also know that momentum
`p prop mv`
Hence, `(p_1)/(p_2) = (m_1 v_1)/( m_2 v_2) = ((r_1)/(r_2))^5`
`(p_1)/(p_2) =((1)/(2))^5`
`p_1: p_2 = 1:32`