NDA 1 2024 GAT, question 84

Topic: Physics

Q84

Escape speed from the Earth is close to $11.2\text{ km s}^{-1}$ . On another planet whose radius is half of the Earth's radius and whose mass density is four times that of the Earth, the escape speed in $\text{km s}^{-1}$ will be close to :

(a) $11.2$ Correct answer
(b) $15.8$
(c) $5.6$
(d) $7.9$

Solution.

Answer: (a) $11.2$

Escape speed is √(2GM/R).
For a sphere of mean density ρ, M is proportional to ρR³, so escape speed is proportional to R√ρ.
The new-to-Earth ratio is (1/2)√4 = 1.
The speed remains 11.2 km/s.