Gravitation

JEE Main level, single correct, medium

106 of 223

Question 106 of 223

The escape velocity from a spherical planet AA is 10 km/s10 \mathrm{~km} / \mathrm{s}. The escape velocity from another planet BB whose density and radius are 10%10 \% of those of planet AA, is ____\_\_\_\_ m/s\mathrm{m} / \mathrm{s}.

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Answer: (D) 10010100 \sqrt{10}

Escape velocity ve=R8πGρ3∝Rρv_e = R\sqrt{\frac{8\pi G\rho}{3}} \propto R\sqrt{\rho}.
Planet B: ρB=0.1ρA\rho_B = 0.1\rho_A, RB=0.1RAR_B = 0.1R_A.
vBvA=0.1RA0.1ρARAρA=0.10.1=11010\frac{v_B}{v_A} = \frac{0.1R_A\sqrt{0.1\rho_A}}{R_A\sqrt{\rho_A}} = 0.1\sqrt{0.1} = \frac{1}{10\sqrt{10}}.
vB=10×11010=110v_B = 10 \times \frac{1}{10\sqrt{10}} = \frac{1}{\sqrt{10}} km/s =100010=10010= \frac{1000}{\sqrt{10}} = 100\sqrt{10} m/s.

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