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14/09/2021 11:35 am
Topic starter
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:
(1) v
(2) 2v
(3) 3v
(4) 4v
1 Answer
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14/09/2021 11:42 am
Correct answer: (4) 4 v
Explanation:
ve = \(\sqrt{\frac{2GM}{R}}\) = \(\sqrt{\frac{2G}{R} \times \frac{4}{3}\pi R^3 \rho}\)
= \(\sqrt{\frac{8 \pi G \rho}{3}R^2}\)
⇒ ve ∝ R
⇒ \(\frac{v_e}{v}\) = \(\frac{4R}{R}\)
⇒ ve = 4v