The ratio of escape velocity of a planet to the escape velocity of earth will be:-
Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.

Solution

Physics sir · 3 steps

Escape velocity goes as the square root of M over R, so take the ratio and let G cancel.

1. Escape velocity formula. For a planet of mass M and radius R, the escape velocity from its surface is vₑ = √(2GM/R). Only M and R change from planet to planet.

   vₚ/vₑ = √(Mₚ/Mₑ×Rₑ/Rₚ)

2. Put in numbers. Mₚ/Mₑ = 16 and Rₑ/Rₚ = 1/4. So vₚ/vₑ = √(16 × 1/4) = √4 = 2.
3. So. The planet's escape velocity is twice the earth's, a ratio of 2 : 1, which is option (d).

The idea to keep. Escape velocity depends on √(M/R). Form the ratio first, cancel 2G, and do not forget the square root at the end.

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