$A$ heavy hollow cone of radius $R$ and height $h$ is placed on a horizontal table surface,with its flat base on the table. The whole volume inside the cone is filled with water of density $\rho$. The circular rim of the cone's base has a watertight seal with the table's surface and the top apex of the cone has a small hole. Neglecting atmospheric pressure,find the total upward force exerted by water on the cone.

Assertion $(A)$: $A$ helium-filled balloon does not rise indefinitely in the air but halts after a certain height.
Reason $(R)$: Viscosity opposes the motion of the balloon. Choose any one of the following four responses:

$A$ solid sphere of specific gravity $27$ has a concentric spherical cavity and it just sinks in water. The ratio of the cavity radius to the outer radius of the sphere is

$A$ wooden cylinder floats vertically in water with half of its length immersed. The density of wood is

$A$ 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: $1 \, \mu m = 10^{-6} \, m$)

$A$ wax candle floats vertically in a liquid of density twice that of wax. The candle burns at the rate of $4\ cm/hr$. Then, with respect to the surface of the liquid, the upper end of the candle will: