Question

With what velocity should a particle be projected so that its height becomes equal to the radius of Earth?

a. Escape velocity
b. Half the escape velocity
c. Double the escape velocity
d. No velocity required

Answer 1

The velocity at which a particle should be projected to achieve a height equal to Earth's radius is the escape velocity itself, which is 11.2 km/s.

Therefore, the correct answer is a. Escape velocity.

Step-by-step explanation:

The question at hand is regarding the velocity required for a particle to reach a height equal to the radius of Earth. In terms of escape velocity, this is a concept in physics related to the speed that an object needs to be projected to break free from a planet's gravitational pull without further propulsion. The given options suggest varying velocities relative to Earth's escape velocity.

Given that the escape velocity from Earth is 11.2 km/s, the velocity required for a particle to reach a height equal to Earth's radius would still be the escape velocity itself, as escaping Earth's gravitational influence encompasses clearing its entire radius and more.

Therefore, to achieve a height equal to the radius without falling back to Earth, an object should be projected at the escape velocity.

Escape velocity is the minimum velocity an object needs to escape the gravitational pull of a planet. It is necessary for an object to overcome the Earth's gravitational force to reach a height equal to the radius of Earth.