What is escape speed?.How Escape speed √(2GM/R)=√(2gR)?

The velocity required for an object to escape from the gravitational influence of the planet is known as escape velocity or escape speed

Expression for escape speed:

   Consider a body of mass 'm' projected vertically upwards from the surface of the earth with velocity v_e. In other to escape from the gravitational pull of the earth ,the body should be given kinetic energy which is equal to the potential energy of the body.

Gravitational potential energy = -GMm / R

Kinetic energy =1/2 mv_e²

----> 1/2 mv_e² = GMm / R

----> 1/2 v_e² = GM / R

----> V_e² = 2GM / R

But g = GM / R²

----> GM = gR²

Substituting the value;

----> v_e² = 2/R (gR²) = 2gR

----> v_e² = under root 2gR

put value of V_e FOR RWEUIRED RELATION

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