Find the kinetic energy required to project a | vedclass

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(A) The kinetic energy required to project an object to infinity is equal to the magnitude of its gravitational potential energy at the surface of the

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$mgR$

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(A) The kinetic energy required to project an object to infinity is equal to the magnitude of its gravitational potential energy at the surface of the Earth.The gravitational potential energy at the surface of the Earth is $U = -\frac{GMm}{R}$.Since $g = \frac{GM}{R^2}$,we have $GM = gR^2$.Substituting this into the potential energy expression: $U = -\frac{(gR^2)m}{R} = -mgR$.Therefore,the required kinetic energy $K = |U| = mgR$.

Find the kinetic energy required to project an object of mass $m$ from the surface of the Earth to infinity.

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