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) = ( 2 r^(2) (rho - sigma )g)/(9eta )`
`r^(2) =(9eta Vt)/(2(rho - sigma )g)`
` ((r_(1))/(r_(2)))^(2) =(rho ^(2) - sigma )/( rho_(1)- rho ) =( (11-2) xx10^(3))/( (8-2)xx10^(3))=(9)/(6) =(3)/(2)`
` (r_(1))/(r_(2))=sqrt((3)/(2)) `