$A$ vessel containing a liquid has a constant acceleration of $19.6 \, m/s^2$ in the horizontal direction. The free surface of the water gets sloped with the horizontal at an angle of ..........

$A$ light semi-cylindrical gate of radius $R$ and length $l$ is pivoted at its midpoint $O$ of the diameter as shown in the figure,holding liquid of density $\rho$. The force $F$ required to prevent the rotation of the gate is equal to:

$A$ vessel containing water is moving with a constant speed towards the right along a straight horizontal path. Which of the following diagrams represents the surface of the liquid?

State whether the following statements are True or False:
$(i)$ In incompressible flow,the density of a fluid changes with time and position.
$(ii)$ Non-viscous flow can be a streamline flow.
$(iii)$ In a steady flow,the velocity of the fluid at each point remains identical with time.

$27$ equal small water drops combine to form a big drop. If the surface tension of water is $T$ and the radius of a small drop is $r$,then:
$(A)$ The excess pressure inside the big drop is three times the excess pressure inside the small drop.
$(B)$ Surface energy decreases in this process.
$(C)$ In this process,$72 \pi r^2 T$ energy is released.
$(D)$ The radius of the big drop is $3r$.
The true statements are:

When a soap bubble of radius $0.2 \ mm$ is charged,it experiences an outward electrostatic pressure of magnitude $\frac{\sigma^2}{2 \varepsilon_0}$,where $\sigma = 20 \ \mu C \ m^{-2}$ is the surface charge density. If the excess pressure inside the soap bubble due to the surface tension is same as this electrostatic pressure,then the surface tension of the soap solution is (Given: $\varepsilon_0 = 8.85 \times 10^{-12} \ C^2 \ N^{-1} \ m^{-2}$)