Escape velocity of a body from earth is 11.2 km / s. If the radius of a planet be onethird the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is :

Solution

Physics sir · 3 steps

Escape speed goes as √(M/R), so just find how much M/R changes and take the root.

1. Formula. A body escapes when its kinetic energy equals the gravitational binding energy, 1/2mv² = GMm/R. The mass m of the body cancels, so the escape speed depends only on the planet.

   vₑ = √(2GM/R) ⇒ vₚ/vₑ = √(Mₚ/Mₑ × Rₑ/Rₚ)

2. Put in ratios. Mₚ/Mₑ = 1/6 and Rₑ/Rₚ = 3, so the product is 3/6 = 1/2. That gives vₚ/vₑ = 1/√2.
3. So. vₚ = 11.2/√2 = 11.2/1.414 ≈ 7.9 km s⁻¹, which is option (a).

The idea to keep. For escape speed comparisons, never plug in G. Write v ∝ √(M/R), use the mass and radius ratios, and remember the square root at the end.

Answer from the NTA final answer key. Solution by PrepWiser.