Correct Answer - Option 3 : Equal to 1
CONCEPT:
Escape velocity
- It is the minimum velocity with which a body should be projected from the surface of the planet so that the body reaches infinity.
- It is given as,
\(⇒ v_{e}=\sqrt{\frac{2GM}{R}}\)
Where G = gravitational constant, M = mass of the planet, and R = radius of the planet
CALCULATION:
As we know that the escape velocity from the surface of the earth is given as,
\(⇒ v_{e}=\sqrt{\frac{2GM}{R}}\) -----(1)
Where G = gravitational constant, M = mass of the earth, and R = radius of the earth
- By equation 1 it is clear that the escape velocity depends upon the mass and the radius of the earth but it is independent of the mass, shape, and size of the projected body.
- So the escape velocity for stone A and stone B will be equal.
- Therefore the ratio of the escape velocity of stone A to stone B from the surface of the earth is 1. Hence, option 3 is correct.
