The pressure of confined air is $p$. If the atmospheric pressure is $P$,then

If two liquids of same volume but different densities $\rho_1$ and $\rho_2$ are mixed,then the density of the mixture is given by:

Is pressure a scalar or a vector quantity? Explain.

$A$ person of height $1.65 \,m$ is standing upright. The additional external force required by a blood vessel of length $1 \,cm$, diameter $1 \,mm$ at the feet to balance the pressure compared to a similar blood vessel in the head is (Density of blood $= 1.1 \times 10^3 \,kg \,m^{-3}$, $g = 10 \,ms^{-2}$) (in $\,N$)

How much force is exerted on our body at atmospheric pressure? Explain.

In Guericke's experiment to show the effect of atmospheric pressure,two copper hemispheres were tightly fitted to each other to form a hollow sphere and the air from the sphere was pumped out to create a vacuum inside. If the radius of each hemisphere is $R$ and the atmospheric pressure is $p$,then the minimum force required (when the two hemispheres are pulled apart by the same force) to separate the hemispheres is