Question

The escape velocity for the earth is 11.2 km/s. 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

• A. 280 km/s
• B. 56.0 km/s
• C. 112 km/s
• D. 24 km/s

Answer 1

Answer: (B)

56.0 km/s

Escape velocity of the planet is the velocity thrown at which the object escapes the gravitational potential of the planet.

$⟹\frac{1}{2}m{v}_{esc}^2=\frac{GMm}{R}$

$⟹v=\sqrt{\frac{2GM}{R}}$

$⟹\frac{v^{\prime }}{v}=\sqrt{\frac{M^{\prime }}{M}.\frac{R}{R^{\prime }}}$$=\sqrt{\frac{100}{1}.\frac{1}{4}}=5$

$⟹v^{\prime }=56.0km/s$