The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ____ m/s. [2026]

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Solution

Q.
The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ____ m/s. [2026]

1 $200 \sqrt{5}$

2 $1000$

3 $100 \sqrt{10}$

4 $1000 \sqrt{2}$

Ans.
(3)

$V_{e} = \sqrt{\frac{2 G M}{R}} = \sqrt{\frac{2 G \times ρ \times \frac{4 π R^{3}}{3}}{R}} \Rightarrow V_{e} \propto \sqrt{ρ} \times R$

$\frac{{(V_{e})}_{B}}{{(V_{e})}_{A}} = \sqrt{\frac{ρ_{B}}{ρ_{A}}} \times \frac{R_{B}}{R_{A}} = \sqrt{\frac{0.1 ρ_{A}}{ρ_{A}}} \times (\frac{0.1 R_{A}}{R_{A}})$

$\frac{{(V_{e})}_{B}}{{(V_{e})}_{A}} = \frac{1}{10} \times \frac{1}{\sqrt{10}}$

${(V_{e})}_{B} = \frac{10 \times 1000}{10 \sqrt{10}} = 100 \sqrt{10} m/sec$

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