Question

A planet as a radius “R” and density “P”. The escape velocity of this planet is _____

(a) directly proportional to P

(b) inversely proportional to P

(c) directly proportional to P^1/2

(d) inversely proportional to P^1/2

This question was posed to me during an online exam.

This interesting question is from Gravitation topic in division Gravitation of Physics – Class 11

Answer 1

Right answer is (c) directly proportional to P^1/2

Best explanation: Escape velocity (v) = [(2*G*M)/R] ^1/2

Density (P) = Mass (M) x Volume

M = P / [(4/3) x pi x R^3]

Therefore;

v = [(8 x pi x P x G x R^2) / 3]^1/2.