Good morning friends
please answer my question a
see your question is ( What is escape velocity and derive it also )
best answer will be brainlist
Answers
ESCAPE VELOCITY : When a body is thrown vertically upward from the surface of the earth, the minimum initial velocity of the body is able to overcome the downward pull by the earth and can escape the earth forever is called the escape velocity.
here, we shall not consider the effects of air. suppose a body of mass 'm ' is thrown vertically upward from the surface of the earth.Let the initial velocity of the body be the escape velocity ( Vesc ).
When the body is on the earth's surface , its total energy E₁ = Kinetic energy + potential energy
= 1/2 mv² esc + ( - GmM/ R ) , Where G = universal gravitational constant , M= mass of the earth & R = radius of earth.
Thus, E₁ = 1/ 2 mv² esc - GmM/ R.
When the body moves to infinity and comes to rest there, its total energy ,
E₂ = 1/2 m ( zero ) ² + ( GmM/ ∞ ) = 0 + 0 = 0.
According to the law of conservation of energy ,
E₁=E₂
∴ 1/2 mv²esc - GmM/ R = 0
∴ 1/2 v²esc= GM/R
∴ Vesc =√2GM/R
This is the requried expression.
HOPE SO IT WILL HELP U............