A metal ball `B_(1)` (density `3.2g//"cc")` is dropped in water, while another metal ball `B_(2)` (density `6.0g//"cc")` is dropped in a liquid of density `1.6g//"cc"`. If both the balls have the same diameter and attain the same terminal velocity, the ratio of viscosity of water to that of the liquid is

Options

A. `2.0`
B. `0.5`
C. `4.0`
D. indeterminate due to insufficient data

Answer

B

Explanation

`v_(t1)_=v_(t2)`
`(2)/(9)g(r^2)/(n_w)[sigma_1-rho_w]=(2)/(9)g(r^2)/(n_1)(sigma_2-rho_1)`
`implies(n_w)/(n_1)=(sigma_1-rho_w)/(sigma_2-rho_1)=(3.2-1)/(6-1.6)=(1)/(2)`