Question 81: Gravitation

Question

To project a body of mass $$m$$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $$R_E, g=$$ acceleration due to gravity on the surface of earth):

Accepted Answer

The kinetic energy required to project a body of mass $m$ from the Earth's surface to infinity, also known as the escape kinetic energy, can be calculated using the concept of gravitational potential energy. The escape velocity $v_e$ is the velocity a body must have to escape the gravitational field of the Earth without any further propulsion. The formula for escape velocity is:
$v_e = \sqrt{2gR_E}$
Where $g$ is the acceleration due to gravity on the surface of Earth and $R_E$ is the radius of the Earth. The kinetic energy $K$ required for this is given by:
$K = \frac{1}{2}mv_e^2$
Substituting the escape velocity formula into the kinetic energy formula gives:
$K = \frac{1}{2}m\left(2gR_Eight)$
$K = \frac{1}{2} 	imes 2 	imes mgR_E$
$K = mgR_E$
Therefore, the required kinetic energy to project a body of mass $m$ from Earth's surface to infinity is $mgR_E$. So, the correct answer is:
Option C: $mgR_E$

Answer

$$1 / 2 m g R_E$$

Answer

$$4 m g R_E$$

Answer

$$m g R_E$$

Answer

$$2 m g R_E$$

Gravitation

To project a body of mass $m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is R_E, g=$ acceleration due to gravity on the surface of earth):

Choose the correct answer: