Question

A solid floats submerged in a liquid. When the liquid is heated, which of the following is most likely to happen?

Answer 1

We know that:
$F_B={\rho }_l{V}_{0}g,\frac{\Delta V}{V}=3\alpha \Delta T,\frac{\Delta \rho }{\rho }=-3\alpha \Delta T$
Buoyancy force acting on block is given by
$F_B={\rho }_l{V}_{0}g\frac{\Delta F_B}{F_B}=\frac{\Delta {\rho }_l}{\rho }+\frac{\Delta V_0}{V}$
As
$\frac{\Delta \rho }{\rho }=-3{\alpha }_l\Delta T$
So the density of the liquid will decrease on heating.
$\frac{\Delta V_0}{V}=3{\alpha }_0\Delta T$
Normall ${\alpha }_l>{\alpha }_0$
However, the relative change in volume of the solid will be negligible as compared to that in the density of liquid .
Hence, upthrust acting on the solid will decrease and the solid will sink.
Final answer: (a)