Given below are two statements:
Statement I: For a planet, if the ratio M/R increases, the escape velocity also increases.
Statement II: Escape velocity is independent of planet radius. Choose the correct answer.

Question

Given below are two statements:

Statement I: For a planet, if the ratio M/R increases, the escape velocity also increases.

Statement II: Escape velocity is independent of planet radius. Choose the correct answer.

G1 Physics · Accepted Answer

Escape velocity is vₑ = √(2GM/R) Therefore, vₑ ∝ √(M/R) So if M/R increases, escape velocity increases. But vₑ clearly depends on R, so it is not independent of radius. Hence Statement I is true and Statement II is false. Therefore option B follows.