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Velocity Displacement Relationship

Two solid sph...

Question

Two solid spheres and of equal volumes but of different densities and are connected by a string. They are fully immersed in a fluid of density. 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} < d_{F}

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B

d_{B} < d_{F}

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C

d_{A} > d_{F}

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D

d_{A} + d_{B} = 2 d_{F}

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Solution

The correct options are
A $d_{A} < d_{F}$
D $d_{A} + d_{B} = 2 d_{F}$
Considering equilibrium of each of the sphere,
For sphere A,
$B = W + T$
$⟹ V d_{F} g = V d_{A} g + T$
For sphere B,
$W = B + T$
$⟹ V d_{B} g = V d_{F} g + T$
For T to be positive in the equations,
$d_{B} > d_{F}$
and $d_{A} < d_{F}$
Eliminating $T$ from the equations gives,
$d_{A} + d_{B} = 2 d_{F}$

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