Expression for the escape velocity of a body from the surface of the e

1.	Expression for the escape velocity of a body from the surface of the earth
Answer» Answer: To find: Escape VELOCITY of an object from the earth surface . Concept: Escape velocity is that velocity with which a particle when projected, goes out of the gravitational PULL of a planet (i.e. infinity ) And we have to find the minimum velocity to do so. So on REACHING infinity, both kinetic and Potential energy will be zero. Calculation: So we will be applying Conservation Of Mechanical Energy theorem. Let escape Velocity be v , mass of object be m , mass of Earth be M ,and radius be r. $\therefore \: ke1 + pe1 = ke2 + pe2$ $= > \dfrac{1}{2} m {v}^{2} + ( - \dfrac{gmM}{ r } ) = 0 + 0$ $= > \dfrac{1}{2} m {v}^{2} = \dfrac{gmM}{r}$ $= > {v}^{2} = \dfrac{2gM}{r}$ $= > v = \sqrt{ \dfrac{2gM}{r} }$ So from this Equation, we can clearly understand that escape velocity is not DEPENDENT on the mass of the object. So final answer : $\boxed{ \red{ v \: esc.= \sqrt{ \dfrac{2gM}{r} }}}$