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

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Aicharya · Accepted Answer

Equilibrium of $A$ $ \begin{aligned} V d_F g & =T+W_A \\ & =T+V d_A g \end{aligned} $ Equilibrium of $B$, $ T+V d_F g=V d_B g $ Adding Eqs. (i) and (ii), we get $2 d_f=d_A+d_B$ $\therefore$ Option (d) is correct. From Eq. (i), we can see that $ d_F>d_A \quad \text { [as } T>0 \text { ] } $ $\therefore$ Option (a) is correct. From Eq. (ii) we can see that, $ d_B>d_F $ $\therefore$ Option (a) is correct. $\therefore$ Correct options are (a), (b) and (d). Analysis of Question Question is moderately difficult but conceptwise it is good

Two solid spheres $A$ and $B$ of equal volumes but of different densities $d_A$ and $d_B$ are connected by a…

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