Question

Why is the value of the constant g different on Earth and on the Moon? Explain in detail.

Short answer

The acceleration due to gravity varies with different bodies to bodies because it depends on the mass and radius of the body. For example, acceleration due to gravity on the Moon is$1.625m/s^2$ and acceleration due to gravity on the Earth is $9.8m/s^2$

Step-by-step solution

Define acceleration due to gravity 

Acceleration due to gravity is defined as the gravitational force acting on the massive body when a freely falling object experiences acceleration and is represented by measured using an SI unit$m/s^2$ The value of acceleration due to gravity depends on the mass and radius of a massive body.

Calculating acceleration due to gravity on the moon and earth

The acceleration due to gravity formula is given by,

$g=\frac{GM}{R^2}....................................\left(1\right)$

Where G is the universal gravitational constant $G=6.674\times {10}^{-11}{m}^3/kg.s^2$.

M = mass of the massive body.

R= radius of the massive body.

For Moon,

$$\begin{gathered} M=7.35\times {10}^{22}kg \\ R=1.74\times {10}^{6}m \end{gathered}$$

Substituting the above value in the equation(1), we get,

$$\begin{gathered} g=\frac{\left(6.67\times {10}^{-11}{m}^3/kg.s^2\right)\left(7.35\times {10}^{22}kg\right)}{\left(1.74\times {10}^{6}m\right)} \\ g=1.625m/s^2 \end{gathered}$$

For Earth,

$$\begin{gathered} M=6\times {10}^{24}kg \\ R=6.4\times {10}^{6}m \end{gathered}$$

Substituting the values in the equation (1), we get

$$\begin{gathered} g=\frac{\left(6.67\times {10}^{11}m/kg.s^2\right)\left(6\times {10}^{24}kg\right)}{\left(6.4\times {10}^{6}m\right)} \\ g=9.8m/s^2 \end{gathered}$$

Thus, the acceleration due to gravity varies with different bodies to bodies because it depends on the mass and radius of the body. For example, g on the Moon is $1.625m/s^2$ , and g on the Earth is$9.8m/s^2$