Question

What is escape velocity? Obtain an expression for it.

Answer 1

Escape velocity is the minimum velocity with which a body must be projected vertically upward so that it may just escape the surface of the Earth.

Answer 2

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❤⭐ESCAPE VELOCITY ⭐❤

• The minimum velocitu required for an object to escape from the gravitational influence of a planet is known as escape velocity.

❤⭐EXPRESSION ⭐❤

Consider an object of mass 'm' at rest on the surface planet of mass M and radius R .

The gravitational potential on the surface of a planet = - GM / R -------1

The gravitational potential energy of the system = gravitational potential × mass of the object = -GMm/R --------2

The object can be made to escape from the gravitation field of the planet by imparting certain minimum speed to the object.

This minimum speed to be imparted to the bound object at rest is escape velocity Ve.

The kinetic energy imparted to the object must be equal and opposite to the potential energy of the system so that the total energy is equal to zero.

1/2 mVe^2 = - [-GMm/R)

= 1/2mVe^2 = GMm/R = Ve^2 = 2GM/R.

== Ve = underroot of 2GM/R

= Underroot of 2gR^2 /R ( GM = gR^2)

Ve= underroot of 2gR.