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:

Two points $A$ and $B$ are at the same depth in a liquid at rest. Then the pressure on them $P_A$ ........... $P_B$.

Give the names of physical quantities which are needed to describe a fluid.

Two cylindrical vessels $A$ and $B$ of different areas of cross-section kept on the same horizontal plane are filled with water to the same height. If the volume of water in vessel $A$ is $3$ times the volume of water in vessel $B$,then the ratio of the pressures at the bottom of the vessels $A$ and $B$ is

When two metals of equal volume are mixed,the relative density of the mixture is $4$. When equal masses of these two metals are mixed,the relative density of the mixture is $3$. What are the relative densities of the two metals?

An open-ended $U$-tube of uniform cross-sectional area contains water (density $10^3 \ kg \ m^{-3}$). Initially,the water level stands at $0.29 \ m$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800 \ kg \ m^{-3}$ is added to the left arm until its length is $0.1 \ m$,as shown in the schematic figure. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is-