Question

On what factors does the escape velocity of the rocket depend?
A. Mass of the rocket
B. Mass of the satellite
C. Radius of the earth
D. Speed of the rocket

Answer 1

Hint: As we all know that when a rocket is launched, it moves with a certain speed while it is going outside the atmosphere of the earth. An ample amount of energy is supplied by the fuel in the rocket to take the rocket out from the earth’s atmosphere. The energy that is supplied is more the gravitational potential energy. When the energy supplied exceeds the gravitational potential energy then the rocket leaves the earth’s atmosphere without spending much fuel.

Complete step by step solution:
When the sum of the kinetic energy of the object and the object’s gravitational potential energy is zero, then the velocity of the object at this corresponding equilibrium is called the escape velocity. After gaining the escape velocity, then the object does not accelerate further and the object moves with constant velocity without spending much fuel. It is given by,
${V_e} = \sqrt {\dfrac{{2GM}}{r}} $
Here ${V_e}$ is the escape velocity, $G$ is the universal gravitational constant, $M$ is the mass of the planet and $r$ is the radius of the planet.
So from the above equation, we can conclude that the escape velocity depends on the radius of the planet.

$\therefore$ The escape velocity of the rocket depends on the radius of the planet. Hence, Option (C) is correct.

Note:
One thing to keep in mind here is that in the escape velocity formula, the only one thing that is absent is the mass of the moving object. The escape velocity depends upon the mass and size of the massive objects from which some small moving object is trying to escape.