Question

A spherically uniform planet of mass $8 \times 10^{24}\, kg$ and of radius $6 \times 10^{6}\, m$ is orbiting around the Sun. The escape velocity for the planet is close to (Take $G = 6 \times 10^{-11} \; N -m^2 / kg^2$)

• A. 11.2 km/s
• B. 16 km/s
• C. 4 km/s
• D. 12.6 km/s
• E. 1.6 km/s

Answer 1

Answer: (D)

$K E_{s}+U_{s}=K E_{\infty}+U_{\infty}$
As, we know escape velocity of a planet of mass $M$ and radius $R$ is
$v_{e}=\sqrt{\frac{2 G M}{R}}$
Given, $M=8 \times 10^{24} kg , R=6 \times 10^{6} m$
and $G=6 \times 10^{-11} Nm ^{2} kg ^{-2}$
$v_{e} =\sqrt{\frac{2 \times 6 \times 10^{-11} \times 8 \times 10^{24}}{6 \times 10^{6}}}$
$=\sqrt{160}\,km / s =12.6\,km / s$