Escape velocity of a body from earth is 11.2 km/s. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is

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Solution

Q.
Escape velocity of a body from earth is 11.2 km/s. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is [2024]

1 11.2 km/s

2 8.4 km/s

3 4.2 km/s

4 7.9 km/s

Ans.
(4)

$R_{P} = \frac{R_{E}}{3},$ $M_{P} = \frac{M_{E}}{6}$

$V_{e} = \sqrt{\frac{2 G M}{R}}$ for earth

$V_{e}^{'} = \sqrt{\frac{2 G (M / 6)}{(R / 3)}} = \sqrt{\frac{G M}{R}}$ for planet

$\sqrt{2} V_{e}^{'} = V_{e}$

$V_{e}^{'} = \frac{V_{e}}{\sqrt{2}} = \frac{11.2}{\sqrt{2}} = (11.2) \times 0.7$ km/sec

$V_{e}^{'} = 7.84 k m / s e c \approx 7.9 k m / s e c$

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