An open cubical tank was initially fully filled with water. When the tank was accelerated on a horizontal plane along one of its sides,it was found that one-third of the volume of water spilled out. The acceleration was:

$A$ slender homogeneous rod of length $2L$ floats partly immersed in water,being supported by a string fastened to one of its ends,as shown. The specific gravity of the rod is $0.75$. The length of the rod that extends out of water is:

$A$ glass tube of uniform cross-section is filled with water and mounted on a rotatable shaft as shown in the figure. If the tube is rotated with a constant angular velocity $\omega$,then:

Two identical cylindrical vessels with their bases at the same level each contain a liquid of density $\rho$. The height of the liquid in one vessel is ${h_1}$ and that in the other vessel is ${h_2}$. The area of either base is $A$. The work done by gravity in equalizing the levels when the two vessels are connected is:

$A$ 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 ...... $^o$.

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: $\varepsilon_0 = 8.85 \times 10^{-12} \ C^2 \ N^{-1} \ m^{-2}$)