A sphere of radius R and density `rho_1` is dropped in a liquid of density `sigma`. Its terminal velocity is `v_1`. If another sphere of radius `R` and density `rho_2` is dropped in the same liquid, its terminal velocity will be:

Options

A. `((rho_2-sigma)/(rho_1-sigma))v_1`
B. `((rho_1-sigma)/(rho_1-sigma))v_1`
C. `((rho_1)/(rho_2))v_1`
D. `((rho_2)/(rho_1))v_1`

Answer

A

Explanation

`6pietaRv_1=(4)/(3)piR^3(rho_1-sigma)`
`6pietaRv_2=(4)/(3)piR^3(rho_2-sigma)`
`(v_2)/(v_1)=((rho_2-sigma)/(rho_1-sigma))`