Escape Velocity on a Different Planet – Rankers Physics

Gravitational Potential Energy: Practice Problem & Solution

The escape velocity from the Earth's surface is \(v\). The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is
\(4v\)
\(v\)
\(2v\)
\(3v\)

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:

Escape velocity is given by \(v_e = R\sqrt{\frac{8\pi G\rho}{3}}\). Since the mass density \(rho\) is the same, \(v_e\) is directly proportional to radius \(R\). Therefore, \(v_e' = 4v\).

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