Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

Solution

Physics sir · 3 steps

Escape speed goes as root of M over R, so take the ratio of planet to earth and the constants drop out.

1. Escape velocity formula. A body escapes when its kinetic energy equals the gravitational binding energy, which gives vₑ = √(2GM/R). So vₑ ∝ √(M/R).
2. Set up the ratio. Earth has M_E = 8M_P and R_E = 2R_P. Divide the planet's formula by the earth's, and G and the 2 cancel.

   v_P/v_E = √(M_P/M_E×R_E/R_P) = √(1/8× 2) = √(1/4) = 1/2

3. So. v_P = 1/2× 11.2 = 5.6 km s⁻¹, which is option (c).

The idea to keep. For escape speed, think vₑ ∝ √(M/R). Form the ratio between the two bodies so G cancels, and never forget the square root.

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