$A$ body of volume $V$ floats on water with $\frac{1}{3}$ of its volume above the surface. The volume of the object above the surface when floating on a liquid of specific gravity $1.5$ is

$A$ vessel filled with water is kept on a weighing pan and the scale is adjusted to zero. $A$ block of mass $M$ and density $\rho$ is suspended by a massless spring of spring constant $k$. This block is submerged into the water in the vessel. What is the reading of the scale?

$A$ cube having a side of $10 \ cm$ with unknown mass $m$ and a $200 \ g$ mass were hung at two ends of a uniform rigid rod of $27 \ cm$ length. The rod along with the masses was placed on a wedge,keeping the distance between the wedge point and the $200 \ g$ weight as $25 \ cm$. Initially,the masses were not in balance. $A$ beaker is placed beneath the unknown mass and water is added slowly to it. At a given point,the masses were in balance and half the volume of the unknown mass was submerged in the water. (Take the density of the unknown mass to be greater than that of water,the mass did not absorb water,and the water density is $1 \ g/cm^3$). The unknown mass $m$ is . . . . . . $kg$.

Two rods of the same material and length have their electric resistance in the ratio $1:2$. When both rods are dipped in water,the correct statement will be:

$A$ block of volume $V$ and density $\sigma_b$ is placed in a liquid of density $\sigma_l$ (where $\sigma_l > \sigma_b$). If the block is moved upward by a height $h$ while remaining completely submerged in the liquid,what is the increase in the gravitational potential energy of the system?

$A$ sphere of diameter $7 \, cm$ and mass $266.5 \, g$ floats in a bath of a liquid. As the temperature is raised,the sphere just begins to sink at a temperature $35^{\circ} C$. If the density of the liquid at $0^{\circ} C$ is $1.527 \, g/cm^3$,then neglecting the expansion of the sphere,the coefficient of cubical expansion of the liquid is: