Gravitational Potential Energy — Prelims Questions

A satellite of mass $m$ is orbiting the Earth (mass $M_E$, radius $R_E$) in a circular orbit of radius $r$. What is the total mechanical energy of the satellite?

The work done in slowly lifting a body of mass $m$ from the Earth's surface to a height equal to the radius of the Earth ($R_E$) is:

A particle is projected from the surface of Earth with a speed equal to the escape velocity. What is its total mechanical energy at infinity?

Two particles of masses $m_1$ and $m_2$ are initially at rest at infinite separation. They move towards each other under mutual gravitational attraction. When their separation is $r$, what is their relative speed?

A body of mass $m$ is placed on the surface of Earth. If $R_E$ is the radius of Earth and $M_E$ is its mass, what is the change in potential energy if the body is moved from the surface to the center of the Earth (assuming uniform density)?

A particle is dropped from a height $h$ above the Earth's surface. If $R_E$ is the radius of Earth, the velocity with which the particle strikes the Earth is: