Gravitational Potential Energy at Height Re – Rankers Physics

Gravitational Potential Energy: Practice Problem & Solution

The gravitational potential energy of a body of mass \(m\) at the earth's surface is \(-mgR_e\). Its gravitational potential energy at a height \(R_e\) from the earth's surface will be (Here \(R_e\) is the radius of the earth)
\(-2mgR_e\)
\(2mgR_e\)
\(\frac{mgR_e}{2}\)
\(\frac{-mgR_e}{2}\)

Solution Explained:

To solve this problem, we apply the core principles of Gravitational Potential Energy. Understanding the underlying formula is key to arriving at the correct answer below:

At the surface, \(U_s = -\frac{GMm}{R_e} = -mgR_e\). At a height \(h = R_e\), the distance from the center is \(r = 2R_e\). Thus, \(U_h = -\frac{GMm}{2R_e} = \frac{-mgR_e}{2}\).

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