Show that `P = frac(1)(3)rho c^2` is dimensionally correct where P= Pressure, C = speed, `rho = density`.

Show that the equation s = ut + frac(1)(2)at^2 is dimensionally correct.

Show that the escape velocity of a body from the surface of a planet of radius R and mean density rho is Rfrac(sqrt8pirhoG)(3) OR Show that the escape velocity of a body from the surface of the earth is 2Rfrac(sqrt2pirhoG)(3) , where R is the radius of the earth and rho is the mean density of the earth. OR Obtain formula of escape velocity of a body at rest on the earth's surface in terms of mean density of erth.

Show that frac{1-2i}{3-4i} + frac{1+2i}{3+4i} is a real

Assume that the speed (v) of sound in air depends upon the pressure (P) and density rho of the air and use dimensional analysis to obtain an expression for the speed of sound.

The period T of a soap bubble under SHM is given by T = P^(a) D^(b) S^(c ) , where P is pressure, D , is density and S is surface tension. Then the values of a,b and c are

v = at + frac(b)(t+c) + v_0 is dimensionally valid equation Obtain the dimensional formula for a,b,c where v is velocity, t is time and vunderset(0) is initial velocity.

Consider the following equation of Bernoulli's theorem. P + (1)/(2) rho v^(2) + rhogh = K (constant) The dimensions of K/P are same as that of which of the following

Show that dy/dx = frac{y}{x} in the following, where a and p are constants.: x^p y^4 = (x+y)^(p+4) , p in N

Prove that the critical velocity or Orbital velocity for a satellite orbiting. each in terms of density of the earth is 2Rsqrtfrac(2pirhoG)(3) , where rho is the density and R is radius of earth and G is gravitational constant.

Show that dy/dx = 'frac{y}{x} in the following, where a and p are constants.: sec frac{ x^5 + y^5 }{ x^5 - y^5 } = a^2