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 lt d_F `
B. `d _B gt d _F `
C. `d _ A gt d_F `
D. `d_A + d _B = 2 d_F `

Answer

A, B, D

Explanation

Let V be volume of each sphere and T be the tension in the string. For the string to be taut,
`d_(F)Vggtd_(A)Vg" "rArr" "d_(F)gtd_(A)`
and `d_(B)Vggtd_(F)Vg" "rArr" "d_(B)gtd_(F)`
For equilibrium,
`d_(F)Vg+d_(F)Vg+T`
`=T+d_(A)Vg+d_(E)Vg" "or" "d_(A)+d_(B)=2d_(F)`