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Challenging Physics Problems for Practice: Gravitation

1.

An artificial satellite (mass m) of a planet (mass M) revolves in a circular orbit whose radius is n times the radius R of the planet. The satellite experiences a slight resistance due to cosmic dust. The resistance force is dependent on the satellite velocity as F = a v2, where a is a constant. Calculate how long the satellite will remain in orbit before it falls on to the planet's surface.

2.

Equal masses m hang from strings of different lengths on a balance at the surface of the Earth as shown in the figure. The strings have negligible mass and differ in length by h. Find the error in weighing due to the difference in heights of the masses from the surface. Given that the density of the Earth is .

3.

Assume the Earth to be a uniform sphere of mass M and radius R. Find the pressure P inside the sphere caused by the gravitational compression as a function of r, the distance from the center.

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