If the terminal speed of a sphere of gold (density `=19.5kg//m^3`) is `0.2m//s` in a viscous liquid (density `=1.5kg//m^3`), find the terminal speed of a sphere of silver (density `=10.5kg//m^3`) of the same size in the same liquid

Options

A. `0.2(m)/(s)`
B. `0.4(m)/(s)`
C. `0.133(m)/(s)`
D. `0.1(m)/(s)`

Answer

D

Explanation

Terminal velocity of spherical body in a viscous liquid is given by, `v_(T)=(2r^(2))/(9eta)(rho-sigma)g`
Where `r=` radius of the sphere `rho=` density of the sphere `eta=` coefficient of viscosity,
`sigma=` density of liquid.
`:. vprop(rho-sigma)`
`(v_(g))/(v_(s))=(rho_(g)-sigma)/(rho_(s)-sigma)=(19.5-1.5)/(10.5-1.5)=2`
`:. v_(s)=(v_(g))/(2)=(0.2)/(2)=0.1(m)/(s)`