Increase in Potential Energy – Rankers Physics

Gravitational Potential Energy: Practice Problem & Solution

What is the increase in gravitational potential energy of an object of mass \(m\) raised from the surface of earth to a height equal to \(n\) times of earth radius ?
\(\left(\frac{n+1}{n}\right) mgR\)
\(\left(\frac{n-1}{n}\right) mgR\)
\(\left(\frac{n}{n-1}\right) mgR\)
\(\left(\frac{n}{n+1}\right) mgR\)

Short Solution (Best for NEET):

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:

The increase in potential energy is \(\Delta U = U_f - U_i = -\frac{GMm}{R + nR} - \left(-\frac{GMm}{R}\right) = \frac{GMm}{R} \left(1 - \frac{1}{n+1}\right) = \left(\frac{n}{n+1}\right) mgR\).

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