The area of two holes $A$and $B$are $2a$and $a$respectively. The holes are at height $\left(\frac{H}{3}\right)$ and $\left(\frac{2H}{3}\right)$ from the surface of the water. Find the correct option(s):

A cylindrical vessel of a very large cross-sectional area is containing two immiscible liquids of density ${\rho }_1=600 \mathrm{k}\mathrm{g}/{\mathrm{m}}^3$ and ${\rho }_2=1200 \mathrm{k}\mathrm{g}/{\mathrm{m}}^3$ as shown in the figure.

A small hole having cross-sectional area $5\mathrm{}{\mathrm{c}\mathrm{m}}^2$ is made in right side vertical wall as shown. Take atmospheric pressure as $p_0={10}^5\frac{\mathrm{N}}{{\mathrm{m}}^2}, g=10\mathrm{m}/{\mathrm{s}}^2.$ For this situation, mark out the correct statement(s). (Take cross-sectional area of the cylindrical vessel as $1000{\mathrm{c}\mathrm{m}}^2.$ Neglect the mass of the vessel.)

A rectangular vessel of dimension $\left(l\times b\times h\right)$ and mass $M$ contains a liquid of density $\rho$. The vessel has an orifice at its bottom at a distance $c$ from the rear wall as shown in the figure.

A liquid is filled upto height $h$ in a vessel, as shown. Find correct option(s);

A solid sphere, a cone and a cylinder are floating in water. All have same mass, density and radius. Let $f_1,f_2$ and $f_3$ are the fraction of their volumes inside the water and $h_1,h_2$ and $h_3$ are the depths inside water. Then

The vessel shown in the figure has two sections of the area of cross-section $A_1$ and $A_2$. A liquid of density $\mathrm{\rho }$ fills both the sections, up to height $h$ in each. Neglecting atmospheric pressure.