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. `0.1 ms^(-1)`
B. `1.133 ms^(-1)`
C. `0.4 ms^(-1)`
D. `0.2 ms^(-1)`

Answer

A

Explanation

Velcity `v = (2)/(9)((rho-sigma)r^(2)g)/(eta)`
` v xx (rho-sigma)`
`(v_(1))/(v_(2)) = ((p_(1)-sigma))/((rho_(2)-sigma))`
` (0.2)/(v_(2)) = (19.5 -1.5)/(10.5-1.5)`
`v_(2) = 0.1m//s`