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

Answer

A

Explanation

Terminal speed of spherical body in a viscous liquid is given by
`v_T=(2r^2(rho-sigma)g)/(9eta)`
where `rho=`density of substance of body and
`sigma=`density of liquid.
`(v_T(Ag))/(v_T(gold))=(rho_(ag)-sigma_1)/(rho_(gold)-sigma_1)`
`impliesv_T(Ag)=(10.5-1.5)/(19.5-1.5)xx0.2=(9)/(18)xx0.2`
`=0.1(m)/(s)`