An ideal gas is trapped between a mercury column and the closed lower end of a narrow vertical tube of uniform bore. The upper end of the tube is open to atmosphere (Atmospheric pressure $=76 \mathrm{cm}$ of $Hg$). The lengths of the mercury and the trapped gas columns are $20 \mathrm{cm}$ and $43 \mathrm{cm}$ respectively. What will be the length of the gas column when the tube is tilted slowly in a vertical plane through an angle of $60°$ ? Assume constant temperature all through.

A hollow right circular cone of height $h$ With its base on a horizontal table. With its flat base on the table. The whole volume inside the cone is filled with water of density ρ.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, the total upward force exerted by water on the cone is

A U-tube contains mercury to the same level in both of its arms.If water is poured to a height of $13.6cm$ in one arm, The rise in mercury level in the other arm is $x cm$. Then $x=?$
$\left( density of water={10}^{3}kg{m}^{-3}\right)$