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Two solid spheres A and B of equal volum...

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

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`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
Let V be the volume of each sphere and T is the tension in the string .

For the string to be taut,
`d_F Vg gt D_A Vg`
` rArr d_F gt d_A`
and `d_B Vg gt d_F Vg`
`rArr d_B gt d_F`
for an equilibrium
` d_F Vg + d_F Vg + T = T + d_A Vg + d_B Vg`
or `d_A+ d_B = 2d_F`
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