Two metal spheres are falling through a liquid of density `2xx10^(3)kg//m^(3)` with the same uniform speed. The material density of sphere 1 and sphere 2 are `8xx10^(3)kg//m^(3)` and `11xx10^(3)kg//m^(3)` respectively. The ratio of their radii is :-

Options

A. `(11)/(8)`
B. `sqrt((11)/(8))`
C. `(3)/(2)`
D. `sqrt((3)/(2))`

Answer

D

Explanation

Let `r_(1) and r_(2)` be the radii of sphere 1 and sphere 2 respectively. Then
`v_(1) = (2 r_(1)^(2) (rho_(1) - sigma)g)/(9 eta) and v_(2) = (2 r_(2)^(2) (rho_(2) - sigma)g)/(9 eta)`
According to the given problem,
`v_(1) = v_(2)`
`:. r_(1)^(2) (rho_(1) - sigma) = r_(2)^(2) (rho_(2) - sigma)`
or `(r_(1)^(2))/(r_(2)^(2)) = (rho_(2) - sigma)/(rho_(1) - sigma) = ((11 xx 10^(3) - 2 xx 10^(3)))/((8 xx 10^(3) -2 xx 10^(3))) = (9)/(6) = (3)/(2)`
or `(r_(1))/(r_(2)) = sqrt((3)/(2))`