The terminal speed of a sphere of gold (density = 19.5 kg `m^(-3)`) is 0.2 `ms^(-1)` in a viscous liquid (density = 1.5 kg `m^(-3)`). Then, the terminal speed of a sphere of silver (density = 10.5 kg `m^(-3)`) of the same size in the same liquid is

Options

A. `0.133ms^(-1)`
B. `0.4ms^(-1)`
C. `0.2ms^(-1)`
D. `0.1ms^(-1)`

Answer

A

Explanation

The terminal speed of a small spherical ball of radius r and density `(rho)` in a viscous medium of density `(sigma)` where `rhogtsigma` is given by
`v=(2r^2(rho-sigma)g)/(9eta)`
In this case, `eta`, r and g have the same value in both cases.
`:." "vprop(rho-sigma)`
`:." "(v_("silver"))/(v_("gold"))=(10.5-1.5)/(19.5-1.5)=9/(18)=1/2`
`:." "v_("silver")=(0.2)/(2)=0.1m//s`