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Challenging Physics Problems for Practice: Gravitation

1.

A meteorite of mass m collides with a satellite of mass 10 m. The satellite is orbiting a planet in a circular path of radius R. Due to the collision, the meteorite sticks to the satellite and the satellite goes into an orbit whose minimum distance from the planet is R/2. If the mass of the planet is M, what is the velocity of the meteorite before the collision?

2.

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.

3.

A rocket is fired vertically with a velocity vo. Derive an expression for its velocity v at a height h, given that the radius of earth is R.

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