During constant temperature, we feel colder on a day when the relative humidity is ....... $\%$

The shown $H$-shaped apparatus contains an ideal incompressible liquid and has dimensions as shown in the figure. The diameters of the tubes are small compared to $h$ and $R$. The apparatus is rotated with a constant angular velocity $\omega$ about a symmetric vertical axis as shown in the figure. The pressure at point $A$ is

On opposite sides of a wide vertical vessel filled with water (density $\rho$), two identical holes are drilled, each having cross-section area $A$. The height difference between holes is $x$. The resultant force of reaction of water flowing out of the vessel is ($g$ = acceleration due to gravity).

$A$ drop of water detaches itself from the exit of a tap when $(\sigma=$ surface tension of water, $\rho=$ density of water, $R=$ radius of the tap exit, $r=$ radius of the drop $)$

The radius of an air bubble at the bottom of a lake is $r$,and it becomes $2r$ when the air bubble rises to the top surface of the lake. If $P \text{ cm}$ of water is the atmospheric pressure,then the depth of the lake is: (in $P$)

The vertical limbs of a $U$ shaped tube are filled with a liquid of density $\rho$ up to a height $h$ on each side. The horizontal portion of the $U$ tube having length $2h$ contains a liquid of density $2\rho$. The $U$ tube is moved horizontally with an acceleration $g/2$ parallel to the horizontal arm. The difference in heights in liquid levels in the two vertical limbs,at steady state,will be: