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

Answer

C

Explanation

Terminal speed of spherical body in a viscous liquid is given by
`v_T = (2 r^2(rho - sigma)g)/(9 eta)`
where `rho` = density of substance of body and
`sigma` = density of liquid
From given data
`(v_T(Ag))/(v_T(Gold)) = (rho_(Ag) - sigma_l)/(rho_(Gold) - sigma_l)`
`rArr v_t (Ag) = (10.5 - 1.5)/(19.5 - 1.5) xx 0.2 = (9)/(18) xx 0.2`
=` 0.1 m//s`.