Two solid spheres A and B of equal volumes but of different densities `d_A and d_B` are connected by a string. They are fully immersed in a fluid of density `d_F`. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if

Options

A. `d_(A)ltd_(F)`
B. `d_(B)gtd_(F)`
C. `d_(A)gtd_(F)`
D. `d_(A)+d_(B)=2d_(F)`

Answer

B, D

Explanation

For equilibrium

`d_(A)vg+d_(B)vg=d_(F)vgimpliesd_(F)=(d_(A)+d_(B))/2`
Option `d` is correct to keep the string tight
`d_(B)gtd_(F)` and `d_(A)ltd_(F)`