Fill in the blanks:
$(i)$ The cohesive force between the molecules of liquid is more than the adhesive force between the molecules of the plate, then the angle of contact obtained is ...... (acute/obtuse) and the free surface has a shape of ...... (concave/convex).
$(ii)$ The cohesive force between the molecules of liquid is less than the adhesive force between the molecules of the plate, then the angle of contact obtained is ...... (acute/obtuse) and the free surface has a shape of ...... (concave/convex).
$(iii)$ $A$ large pressure is exerted on the surface of a liquid having a shape of .......... (concave/convex).

$A$ piece of metal weighs $46 \, g$ in air. When it is immersed in a liquid of specific gravity $1.24$ at $27^{\circ}C$,it weighs $30 \, g$. When the temperature of the liquid is raised to $42^{\circ}C$,the metal piece weighs $30.5 \, g$ and the specific gravity of the liquid at $42^{\circ}C$ is $1.20$. Calculate the coefficient of linear expansion of the metal.

Write two parts of fluid mechanics and what studies are made in them?

$A$ cylinder of radius $4 \ cm$ and height $10 \ cm$ is immersed in two liquids as shown. Specific gravity of oil is $0.5$. $2 \ cm$ of the cylinder is in the air. Select the $INCORRECT$ statement. Neglect atmospheric pressure.

$(a)$ It is known that the density $\rho$ of air decreases with height $y$ as $\rho = \rho_{0} e^{-y / y_{0}}$,where $\rho_{0} = 1.25 \; kg \, m^{-3}$ is the density at sea level,and $y_{0}$ is a constant. This density variation is called the law of atmospheres. Obtain this law assuming that the temperature of the atmosphere remains constant (isothermal conditions). Also,assume that the value of $g$ remains constant.
$(b)$ $A$ large $He$ balloon of volume $1425 \; m^{3}$ is used to lift a payload of $400 \; kg$. Assume that the balloon maintains a constant radius as it rises. How high does it rise?
[Take $y_{0} = 8000 \; m$ and $\rho_{He} = 0.18 \; kg \, m^{-3}$]

The cross-sectional area of a horizontal tube increases along its length linearly as we move in the direction of flow. The variation of pressure, as we move along its length in the direction of flow ($x$-direction), is best depicted by which of the following graphs?