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) = 2d_(F)`

Answer

A, B, D

Explanation

For equilibrium
`d_(A)vg + d_(B)vg = d_(F)vg + d_(F)vg`
`rArr d_(F) = (d_(A) + d_(B))/(2) rArr` option `(D)` is correct
`d_(B) gt d_(F)` and `d_(A) lt d_(F)`