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

`v_T=(2r^2 g)/(9)((rho-sigma))/(eta)`
`v_T prop r^2(rho-sigma), v_(T_1)=v_(T_2)`
`implies r_1^2(8-2)xx10^3=r_2^2(11-2)xx10^3`
`implies (r_1)/(r_2)=sqrt(9/6)=sqrt(3/2)`.