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

We have `v = (2)/(9) ((rho - sigma)r^(2)g)/(eta)`
Here we can say
`v prop (rho - sigma)`
`(v_(1))/(v_(2)) = (rho_(1) - sigma)/(rho_(2) - sigma) = 0.1`