Two spheres of equal masses but radii R and 2 R are allowed to fall in a liquid, the ratio of their terminal velocities is

Options

A. 16
B. 8
C. 4
D. 2

Answer

C

Explanation

The terminal velocity is given by v, where `v prop r^(2)`
(r=radius of the sphere).
The mass of the sphere can be given by `m=(4)/(3)pi r^(3)rho`.
Thus `m prop r^(3)`
So, according to the question,
`(m_(1))/(m_(2))=(1)/(8)=((r_(1))/(r_(2)))^(2) implies (r_(1))/(r_(2))=(1)/(2)`
and since, `(v_(1))/(v_(2))=((r_(1))/(r_(2)))^(2)=((1)/(2))^(2)=(1)/(4)=(v)/(nv)=(1)/(4) implies n=4`