Question

The escape velocity of a body on a planet ‘ A ’ is 12 kms–1. The escape velocity of the body on another planet ‘ B ’, whose density is four times and radius is half of the planet ‘ A ’, is

• A. 12 kms–1
• B. 24 kms–1
• C. 36 kms–1
• D. 6 kms–1

Answer 1

Answer: (A)

12 kms–1

Answer 2

Th correct option is(A): 12 kms–1

$v_{esc}=\sqrt\frac{2GM}{R}=\sqrt\frac{2G}{R}×p×\frac{4}{3}{\pi}R^3$

$⇒v_{esc}∝R\sqrt{p}$

$⇒\frac{(v_esc)B}{(vesc)A}=1$

⇒ (v esc)B = 12 km/s