$A$ hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$. The volume of the remaining cylinder is $V$ and mass $M$. It is suspended by a string in a liquid of density $\rho$,where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is

$Assertion$ : $A$ balloon filled with hydrogen will fall with acceleration $\frac{g}{6}$ on the moon.
$Reason$ : Moon has no atmosphere.

$A$ wooden block of outer volume $1 \text{ litre}$ and specific gravity $\frac{3}{4}$ having a cavity floats with half of its volume immersed in water. Then the volume of the cavity is (in $\text{ ml}$)

$A$ 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 air bubble of radius $1\,cm$ in water has an upward acceleration of $9.8\,cm\,s^{-2}$. The density of water is $1\,g\,cm^{-3}$ and water offers negligible drag force on the bubble. The mass of the bubble is $.......g$.
$(g = 980\,cm\,s^{-2})$

$A$ body floats in a liquid contained in a beaker. The whole system,as shown,falls freely under gravity. The upthrust on the body due to the liquid is