A $U$-tube of base length $l$ filled with same volume of two liquids of densities $\rho$ and $2\rho$ is moving with an acceleration $a$ on the horizontal plane. If the height difference between the two surfaces (open to atmosphere) becomes zero, then the height $h$ is given by

A cubical block of side $10 \mathrm{cm}$ floats at the interface of oil and water. The pressure above that of the atmosphere at the lower face of the block is

A large tank is filled with water $($density $={10}^3 \mathrm{kg} {\mathrm{m}}^{-3} )$. A small hole is made at a depth $10 \mathrm{m}$ below water surface. The range of water issuing out of the hole is $R$ on the ground. What extra pressure must be applied on the water surface so that the range become $2 \mathrm{R} ?$ $($take $1 \mathrm{atm}={10}^5 \mathrm{Pa}$ and $\left.g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A wooden plank of length $1 \mathrm{m}$ and uniform cross-section is hinged at one end to the bottom of a tank as shown in the figure. The tank is filled with water up to a height of $0.5 \mathrm{m}$. The specific gravity of the plank is $0.5$. The angle $\theta$ made by the plank in equilibrium position is