Derive an expression for the variation of g with the height from the surface of the Earth.

Derive an expression for the variation of g with the height from the surface of Earth.

Using the law of conservation of energy, derive an expression for the escape velocity of an object from the surface of the earth.

Derive an expression for the escape speed of a body from the surface of the Earth. Express it in terms of the mean density of the Earth.

Discuss the variation of g with height and depth.

Obtain an expression for the acceleration due to gravity on the surface of the earth in terms of mass of the earth and its radius. Discuss the variation of acceleration due to gravity with altitude and depth. If a body is taken to a height R / 4 from the surface of the earth, find percentage decrease in the weight of the body ? Here R is the radius of the earth.

Derive an expression for the acceleration due to gravity at a depth d below the Earth's surface.

The orbital velocity of a satellite is given by the expression V = sqrt((GM)/(R + h)) , here M is the mass of the Earth, R is the radius of the Earth and 'h' is the height of the satellite from the surface of the Earth. Explain the reasons why the geostationary satellite is not possible to set in orbit around the Earth at two different heights from the surface of the Earth.