Work Done to Lift Mass from Planet’s Surface – Rankers Physics

Gravitational Potential Energy: Practice Problem & Solution

If mass of a planet is \(M\) and radius is \(x\), then the work to be done to slowly take a mass \(m\) from surface of planet to a height \(4x\) is :
\(\frac{4GMm}{5x}\)
\(\frac{2GMm}{5x}\)
\(\frac{5GMm}{x}\)
\(\frac{4GMm}{3x}\)

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:

Initial position \(r_i = x\), final position \(r_f = x + 4x = 5x\). Work done \(W = U_f - U_i = -\frac{GMm}{5x} - \left(-\frac{GMm}{x}\right) = \frac{4GMm}{5x}\).

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