Question

Derive an expression for the gravitational potential energy of a system consisting of Earth and a brick of mass m placed at Earth’s center. Take the potential energy for the system with the brick placed at infinity to be zero.

Solution

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In this problem, we need to derive an expression for the gravitational potential energy of a brick-earth system when the brick is placed at the center of the earth.

We will do this using the standard expression for gravitational potential energy:

Ug=0rFgdrU_g=\int _{0} ^{\vec r} \vec F_g \cdot d\vec r

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