Check the correctness of the relation v=scar root 2gm/r
Answers
If you were to escape from the clutches of gravity you would have to distance yourself from the gravitational pull from the object. In order to get this distance, one must have a certain amount of kinetic energy.
The minimum kinetic energy(KE) one must have always equals to gravitational potential energy (PE). The formula for KE = (1/2) m v2, where 'm' is the mass and 'v' is velocity.
If PE = G m M / R, where 'm' is the mass of the object that is trying to escape, 'M' is the mass of the planet that the object is trying to escape from and 'R' is the radius of the planet.
Since 'G' is Newton's Universal Constant Gravitaion then PE=KE we get, G m M / R=(1/2) m v2, the mass of the object being released in the space gets the same velocity and rearranging the equation we get, v2 = 2 G M / R.
Thus, by taking square root on both the sides we get, vesc = Square root (2 G M / R).