$A$ large number of water drops,each of radius $r$,combine to form a single drop of radius $R$. If the surface tension is $T$ and the mechanical equivalent of heat is $J$,then the rise in temperature will be:

Two vessels of equal cross-sectional area $A$ are filled with a liquid of density $d$. The height of the liquid in one vessel is $h_1$ and in the other vessel is $h_2$. When both vessels are connected,find the work done by gravity.

$A$ cylindrical vessel of height $500 \ mm$ has an orifice (small hole) at its bottom. The orifice is initially closed and water is filled in it up to height $H$. Now the top is completely sealed with a cap and the orifice at the bottom is opened. Some water comes out from the orifice and the water level in the vessel becomes steady with the height of the water column being $200 \ mm$. Find the fall in height (in $mm$) of the water level due to the opening of the orifice.
[Take atmospheric pressure $= 1.0 \times 10^5 \ N/m^2$,density of water $= 1000 \ kg/m^3$ and $g = 10 \ m/s^2$. Neglect any effect of surface tension.]

$A$ $U$-tube has a left limb with a cross-sectional area one-quarter that of the right limb. The tube contains mercury (density $13.6 \text{ g/cm}^3$). The level of mercury in the narrow (left) limb is at a distance of $36 \text{ cm}$ from the upper end of the tube. What will be the rise in the level of mercury in the right limb if the left limb is filled to the top with water (in $\text{ cm}$)? (Density of water = $1 \text{ g/cm}^3$)

$A$ container of liquid is released from rest on a smooth inclined plane as shown in the figure. The length of the inclined plane is sufficient. Assume the liquid finally reaches equilibrium relative to the container. The final liquid surface makes an angle with the horizontal of ...... $^o$.

$A$ drop of water breaks into two droplets of equal size. In this process,which of the following statements is correct?