In a $U$-tube as shown in the figure,water and oil are in the left and right sides of the tube,respectively. The heights from the bottom for the water and oil columns are $15 \; cm$ and $20 \; cm$,respectively. The density of the oil is ...... $kg/m^3$. [Take $\rho_{\text{water}} = 1000 \; kg/m^3$]

In making an alloy,a substance of specific gravity $s_1$ and mass $m_1$ is mixed with another substance of specific gravity $s_2$ and mass $m_2$; then the specific gravity of the alloy is

Liquid is ...... while gas is ...... . (Fill in the blank) [incompressible,compressible]

$A$ liquid mixture of volume $V$ has two liquids as its ingredients with densities $\alpha$ and $\beta$. If the density of the mixture is $\sigma$,then the mass of the first liquid in the mixture is ............

In the arrangement shown, both the vessels $A$ and $B$ are identical, but the amount of water in $B$ is double that in $A$. The vessels are closed by identical leak-proof pistons at the same height. The pistons are connected to the ends of a lever arm. There is no friction between the pistons and the container walls. The system is in equilibrium in the situation shown. Now, the valve in the horizontal tube connecting both the vessels is opened. In which direction will the water flow through the tube?

$A$ vertical triangular plate $ABC$ is placed inside water with side $BC$ parallel to the water surface as shown. The force on one surface of the plate by water is (density of water is $\rho$ and atmospheric pressure is $P_0$).