Test on Gravitation

Derivation

1. Derive the formula for the acceleration due to gravity at the distance of r from the center of the earth where $0<r<R_E$.
2. Derive the formula for the gravitational force on an object of mass m due to Mars placed at a depth of d below its surface. Given that mass of the Mars is $M_M$ and its radius is $R_M$.
3. Derive the formula for the escape velocity from the planet Jupiter. Given that mass of the Jupiter is $M_J$ and its radius is $R_J$.

Numerical

1. Find the acceleration due to gravity at a depth of 1200 km and at a height of 1200 km. Compare the results.

Concepts

1. What do you mean by the principle of superposition of gravitational forces. Explain with suitable diagram.