Prove that g = `GM/R^2` , where M is mass and R is radius of earth.

Check the correctness of the physical relation: v= sqrt((2GM)/(R)) , where v is velocity, G is gavitational constant, M is mass and R is radius of the earth.

Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR^2//5 , where M is the mass of the sphere and R is the radius of the sphere.

At what height above the earth surface, the acceleration due to gravity will be half that on the surface of earth ? Suppose R is the radius of earth.

Prove that r^1 = 1 + 2/n where n is number of degrees of freedom.

A satellite is in an elliptic orbit around the earth with aphelion of 6R and perihelion of 2R where R = 6400 km is the radius of the earth. Find eccentricity of the orbit. [G = 6.67 xx 10^-11 SI units and M = 6xx 10^24 kg]

At what altitude in metre will the acceleration due to gravity be 25% of that at the earth's surface? (R is the radius of the earth)

G.M of 8 and 18 is:

Prove that "^nP_r= ^nC_r ^rP_r .

An artificial satellite is revolving around a planet fo mass M and radius R, in a circular orbit of radius r. From Kepler's third law about te period fo a satellite around a common central bdy, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show usingn dimensional analysis, that T = k/R sqrt((r^3)/(g)) , where k is a dimensionless constant and g is acceleration due to gravity.

Electric field inside a sphere varies with distance as A r. Find the total charge enclosed within the sphere, if A = 3,000 V m^-2 and R = 30 cm, where R is radius of the sphere.