Question

The mass of the earth is $9$ times that of Mars. The radius of the earth is twice that of Mars. The escape velocity on earth is $12km/sec$. The escape velocity on Mars is ......... km/sec.

• A. $8\sqrt{2}$ km/sec
• B. $2\sqrt{2}$ km/sec
• C. $6\sqrt{2}$ km/sec
• D. $4\sqrt{2}$ km/sec

Answer 1

Answer: (D)

Escape speed is $v_e=\sqrt{\frac{2GM}{R}}=12$ km/s on Earth's surface.
Now, the mass of Mars is one-ninth and radius is half that of Earth's.
So,
$v_m^{{}^{\prime }}=\sqrt{\frac{2G\times M/9}{R/2}}=\frac{\sqrt{2}}{3}\times \sqrt{\frac{2GM}{R}}=\frac{\sqrt{2}}{3}\times 12=4\sqrt{2}$ km/s