$A$ wooden block floats in a liquid with $40\%$ of its volume inside the liquid. When the vessel containing the liquid starts rising upwards with an acceleration $a = g/2$, the percentage of volume inside the liquid is ......... $\%$

An object weighs $m_1$ in a liquid of density $d_1$ and $m_2$ in a liquid of density $d_2$. The density $d$ of the object is

$A$ 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 . . . . . . $kg$.

An ice cube contains a large air bubble. The cube is floating on the horizontal surface of water contained in a trough. What will happen to the water level when the cube melts?

$A$ machine is blowing spherical soap bubbles of different radii filled with helium gas. It is found that,if the bubbles have a radius smaller than $1 \, cm$,then they sink to the floor in still air. Larger bubbles float in the air. Assume that the thickness of the soap film in all bubbles is uniform and equal. Assume that the density of soap solution is same as that of water $\left(= 1000 \, kg \, m^{-3}\right)$. The density of helium inside the bubbles and air are $0.18 \, kg \, m^{-3}$ and $1.23 \, kg \, m^{-3}$,respectively. Then,the thickness of the soap film of the bubbles is .......... $\mu m$ (Note: $1 \, \mu m = 10^{-6} \, m$)

What is buoyancy?