Drops of liquid of density $d$ are floating half immersed in a liquid of density $\rho$. If the surface tension of the liquid is $T$, then the radius of the drop is

$A$ $U$-tube of small and uniform cross-section contains water of total length $4H$. The height difference between the water columns on the left and on the right is $H$ when the valve $K$ is closed. The valve is suddenly opened,and water flows from left to right. Ignore friction. The speed of the water when the heights of the left and the right water columns are the same is:

$A$ cylindrical container is filled with liquid. When the container is rotated about its axis,the liquid rises along its sides. If the radius of the container is $r$ and the angular velocity of the container is $\omega$ rad/s,what will be the difference in the height of the liquid at the center and at the sides?

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 $P$)

$A$ uniform meter scale is supported at its $20 \ cm$ mark. $A$ body suspended from the $10 \ cm$ mark keeps the scale horizontal. However,the scale becomes unbalanced if the body is completely immersed in water. To regain the balance,the body is shifted to the $8 \ cm$ mark. Therefore,the specific gravity of the material of the body is

$A$ long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis,the liquid rises up near the wall. If the radius of the vessel is $5 \, cm$ and its rotational speed is $2$ rotations per second,then the difference in the heights between the centre and the sides,in $cm$,will be