Uniform speed of 2 cm diameter ball is `20cm//s` in a viscous liquid. Then, the speed of 1 cm diameter ball in the same liquid is

Options

A. `80cms^(-1)`
B. `40cms^(-1)`
C. `10cms^(-1)`
D. `5cms^(-1)`

Answer

D

Explanation

Terminal velocity
`v=2/9(r^2(rho-sigma))/(eta)`
`rArr v prop r^2`
here, `v_1 = 20cms^(-1), r_1 = 2cm, r_2 = 1cm`
`therefore " " v_1/v_2=20/r_2^2 = (2)^2/(1)^2`
`rArr " " v_2=20//4=cms^(-1)`