In the derivation of `P_1-P_2=rhogz` it was asumed that the liquid is incompressible. Why will this equation not be stictly valid for a compressible liquid?

Derive an equation for the total pressure at a depth 'h' below the liquid surface.

Let P_1 denote the equation of a plane to which the vector ( hat i+ hat j) is normal and which contais the line whose equation is vec r= hat i+ hat j+ hat k+lambda( hat i- hat j- hat k)a n dP_2 denote the equation of the plane containing the line L and a point with position vector hat jdot Which of the following holds good? a. The equation of P_1 is x+y=2. b. The equation of P_2 is vec(r) . (i-2j+k) = 2 c. The acute angle between P_1 and P_2 is cot^(-1) sqrt(3) d. The angle between plane P_2 and the line L is tan^(-1) sqrt(3)

A straight line through P(1, 2) is such that its intercept between the axes is bisected at P. Its equation is

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has no real roots. Prove that in this case equation P(P(x))=x has no real roots either.

Two capillaries of radii r_(1)andr_(2) and lengths l_(1)andl_(2) respectively are in series. A liquid of viscosity eta is flowing through the combination under a pressure difference P. What is the rate of volume flow of liquid?

Two capillaries of radii r_(1)andr_(2) and lengths l_(1)andl_(2) respectively are in series. A liquid of viscosity eta is flowing through the combination under a pressure difference P. What is the rate of volume flow of liquid?

The equation omega=(mu_v-mu_r)/(mu-1) was derived for a prism having small refracting angle. Is it also valid for a prism of large refracting angle? Is it also valid for a glass slab or a glass sphere?