Discuss the variation of g (i) with the height above the earth's surface

Discuss the variation of g (ii) with depth below the earth's surface.

Assume that the earth is a uniform sphere of radius R. If the acceleration due to gravity at a height h above the earth's surface is g_1 and at the same depth below the surface of the earth is g_2(h lt R) , then show that, g_2=g_1(1-h/R)(1+h/R)^2 .

The acceleration due to gravity at a height above the earth's surface is ……..than that at the same depth below the surface of the earth. [Fill in the blanks]

Discuss the variation of g with depth. What happens to g at the centre of earth?

If the mass of the earth is 6xx10^(27) g and its radius 6400 km, what will be the acceleration due to gravity at a height 64 km above the earth's surface ? Given that G=6.67xx10^(-8) CGS unit.

A balloon of mass 1000 kg is motionless is the air at some height above the earth's surface. When an object of mass 200 kg is dropped from the balloon, what will be the acceleration with which the balloon starts rising? (g = 9.8 m cdot s^(-2) )

An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. (i) Determine the height of satellite above the earth's surface.

An artificial satellite appears to be stationary with respect to an observer on the earth. At what height (approx.) above the earth's surface is it placed ?