The escape velocity for the earth is 11.2 km/sec. The mass of another planet 100 times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is

56.0 km/sec

280 km/sec

112 km/sec

56 km/sec

Solution

56.0 km/sec

Escape velocity of earth V_e=11.2km/sec

v_escape= $\sqrt{\frac{2 GM}{R}} \propto \sqrt{\frac{M}{R}}$

Hence, $\frac{V_{P}}{V_{e}} = \sqrt{\frac{\frac{M_{p}}{R_{P}}}{\frac{M_{e}}{R_{e}}}} = \sqrt{\frac{M_{P}}{R_{p}} \times \frac{R_{e}}{M_{e}}}$

Or $\frac{V_{p}}{V_{e}} = \sqrt{100 \times \frac{1}{4}} = \sqrt{25} = 5$

V_p=5 $\times$ V_e=5 $\times$ 11.2 =56km/sec

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