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

d_{A} < d_{F}

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d_{B} > d_{F}

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d_{A} > d_{F}

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

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Solution

The correct options are
B $d_{B} > d_{F}$
D $d_{A} + d_{B} = 2 d_{F}$
Since tension is developed in the string, we conclude that $B$ has a tendency to sink and $A$ has a tendency to float individually.

$\Rightarrow d_{A} < D_{F} < D_{B}$

Also since system is in equilibrium

$d_{A} . V 9 d_{B} . V = 2 V . D_{F} \Rightarrow d_{A} + d_{B} = 2 d_{F}$

Archimedes Principle on system in equilibrium

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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

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