Question

The kinetic energy needed to project a body of mass m from the earth's surface (radius.R) to infinity is

Answer 1

the earth's surface to infinity is  mgR.

Answer 2

Answer:

$K.E=mgR$

Explanation:

AS per the question,

Formula for Kinetic energy is given by:

$K.E=\frac{1}{2}mV_{e}^{2}$

$V_{e}$ is the escape velocity.

Since,

Escape velocity of earth is given by:

$V_{e}=\sqrt{2gR}$

Where,

R = radius of the earth

On putting this value in Kinetic energy, we get

$K.E=\frac{1}{2}mV_{e}^{2}$

$K.E=\frac{1}{2}m(\sqrt{2gR})^{2}$

$K.E=\frac{1}{2}m(2gR)$

$K.E=mgR$

Hence, the kinetic energy needed to project a body of mass m from the earth's surface (radius = R) to infinity is $K.E=mgR$.