Increase in potential energy raised to n times radius – 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 ?
\(\left(\frac{n+1}{n}\right) mgR\)
\(\left(\frac{n-1}{n}\right) mgR\)
\(\left(\frac{n}{n-1}\right) mgR\)
\(\left(\frac{n}{n+1}\right) mgR\)

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:

The increase in potential energy is \(\Delta U = \frac{mgh}{1 + h/R}\). Since \(h = nR\), we get \(\Delta U = \frac{mg(nR)}{1 + n} = \left(\frac{n}{n+1}\right) mgR\).

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