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. `v[p_(2)+sigma)//p_(1)+sigma)]`
B. `v[p_(1)+sigma)//p_(2)+sigma)]`
C. `v[p_(2)-sigma)//p_(1)-sigma)]`
D. `v[p_(1)-sigma)//p_(2)-sigma)]`

Answer

C

Explanation

The terminal velocity of the sphere
`v =(2)/(9)R^(2) ((rho^(2) - sigma)g)/(eta)" ".....(i)`
Here ,R = radius of sphere `rho_(1)` = density of sphere and `sigma` = density of liquid .
Now if density of metal sphere is changed to `rho_(2)` then terminal velocity
`v_(2) (2)/(9)(R^(2) (rho_(2) - sigma)g)/((rho_(1) - sigma)) or (v_(2)(rho_(2) - sigma))/((rho_(1) - sigma))`
Hence , the terminal velocity is `(v(rho_(2)-sigma))/(rho_(1)-sigma)`