Question:

If an object of mass m is given a velocity equal to twice the escape velocity of Earth then the velocity of the object at the point where Earth shows no Gravitational force strength would be at?

Updated On: Aug 16, 2023
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Solution and Explanation

The velocity of an object at the point where Earth's gravitational force becomes negligible (far away from Earth) would be zero.
The escape velocity of Earth is the minimum velocity an object needs to escape the gravitational pull of Earth and never return. If an object is given a velocity equal to twice the escape velocity, it means the object has more than enough energy to escape Earth's gravitational field.
As the object moves farther away from Earth, the gravitational force between Earth and the object decreases. At a certain point, the gravitational force becomes negligible compared to other forces acting on the object. This point is often considered to be at an infinite distance from Earth.
At this point, the object's velocity would become zero because there is no gravitational force acting on it. In other words, the object would be moving away from Earth at a decreasing velocity until it eventually comes to rest (velocity equals zero) at an infinite distance from Earth.
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Concepts Used:

Gravitation

In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.

Newton’s Law of Gravitation

According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,

  • F ∝ (M1M2) . . . . (1)
  • (F ∝ 1/r2) . . . . (2)

On combining equations (1) and (2) we get,

F ∝ M1M2/r2

F = G × [M1M2]/r2 . . . . (7)

Or, f(r) = GM1M2/r2

The dimension formula of G is [M-1L3T-2].