Question

The kinetic energy needed to project a body of mass m from the earth' surface to infinity is
(a) 14mgR
(b) 12mgR
(c) mgR
(d) 2 mgR.

Answer 1

The kinetic energy needed to project a body of mass m from the earth' surface to infinity is (C) mgR

Explanation:

The kinetic energy needed to project a body of mass. The kinetic energy needed to project a body from earth's surface to infinity is known as its escape energy.

Escape Velocity(Ve)=$\sqrt2gR$

Kinetic Energy=1/2m$v_{e^{2} }$=1/2 m*2gR=mgR.

Answer 2

The kinetic energy needed to project a body of mass m from the earth' surface to infinity is mgR.

Explanation:

The kinetic energy required for projecting the body mass m from the surface of Earth to infinity is equal to the negative of the body’s potential energy change.

This is shown as kinetic energy = - (-initial potential energy + final potential energy)

$\Rightarrow \mathrm{K}=-\mathrm{GMmR}-\mathrm{GMmR}^{\prime}$

$\Rightarrow \mathrm{K}=-\mathrm{GMm} \infty-\mathrm{GMmR}$

$\Rightarrow \mathrm{K}=\mathrm{GMR} 2 \times \mathrm{mR}$

Therefore, $\mathrm{g}=\mathrm{GMR} 2$