Question

Escape velocity from a planet is $ {{v}_{e.}} $ If its mass is increased to 8 times and its radius is increased to2 times, then the new escape velocity would be :

• A. $ {{v}_{e.}} $
• B. $ \sqrt{2}{{v}_{e.}} $
• C. $ 2{{v}_{e.}} $
• D. $ 2\sqrt{2}{{v}_{e.}} $

Answer 1

Answer: (C)

Escape velocity $ {{v}_{e}}=\frac{\sqrt{2G{{M}_{e}}}}{{{R}_{e}}} $ New escape velocity $ v_{e}^{'}=\frac{\sqrt{2G(8{{M}_{e}})}}{{{R}_{e}}} $ $ =2\frac{\sqrt{2G{{M}_{e}}}}{{{R}_{e}}}=2{{v}_{e}} $