Question

Explain, why one can jump higher on the surface of the moon than on the earth?

Answer 1

For solving this question, we need to understand the concept of gravity. Gravitational acceleration plays an important role in determining how high we can jump. Therefore, we will compare the gravitational acceleration of the moon and the earth to determine the reason for jumping higher on the surface of the moon than on the earth.

Formula used:
$g = \dfrac{{GM}}{{{R^2}}}$ ,
where, $g$ is the gravitational acceleration, $G$ is gravitational constant, $M$ is the mass and $R$ is the radius of the surface

Complete step by step answer:
We will determine gravitational acceleration of both the earth and the moon.Let ${g_e}$ be the gravitational acceleration on the earth’s surface, ${M_e}$ is the mass of the earth and ${R_e}$ is the radius of the earth.
${g_e} = \dfrac{{G{M_e}}}{{{R_e}^2}}$
Similarly, Let ${g_m}$ be the gravitational acceleration on the moon’s surface, ${M_m}$ is the mass of the moon and ${R_m}$ is the radius of the moon.
${g_m} = \dfrac{{G{M_m}}}{{{R_m}^2}}$
Now, if we take ratio of gravitational acceleration of the moon to that of the earth, we get
$\dfrac{{{g_m}}}{{{g_e}}} = \dfrac{{{M_m}{R_e}^2}}{{{M_e}{R_m}^2}} < 1$
It is clear that this ratio is less than one as the radius of the earth is much higher than the radius of the moon.Therefore, we can say that gravitational acceleration is lower on the moon than on the earth due to which a person experiences less gravitational force on the moon.This is the reason why one can jump higher on the surface of the moon than on the earth.

Note: In this question, we have seen that the gravitational acceleration is lower on the moon’s surface than on the earth’s surface. This value of gravitational acceleration is nearly six times lower on the moon than on the earth. Therefore, a person weighs six times lower on the moon than he weighs on the earth.