Question

Consider two planets P₁ and P₂ of radii R₁ and R₂ respectively, such that R₂ > R₁ and M₂ = M₁. The escape velocity of a satellite 
1. is lesser at P₂ than compared to P₁
2. remains constant for both the planets  P1 and P2
3. is greater at P₂ than compared to  P1
4. None of the above

Answer 1

Correct Answer - Option 1 : is lesser at P₂ than compared to P₁

The correct answer is option 1) i.e. is lesser at P2 than compared to P1

CONCEPT:

• Escape velocity is the minimum velocity with which a body is projected from the surface of the planet so as to reach infinity, by overcoming the pull by gravity.

Escape velocity at the surface of a planet is given by, 

 \(⇒ V_e=\sqrt{\frac{2GM}{R}}\)  

Where G = gravitational constant (6.67 × 10-11 Nm2/kg2), M = mass of the planet and R = radius of the planet.

EXPLANATION:

It is known that R2 > R1 and M2 = M1

Escape velocity, V_e ∝ \(\frac{1}{\sqrt R}\)

• Therefore, escape velocity is lesser at P2 than compared to P1.