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.