Question

Calculate the acceleration due to gravity on the Moon, which has radius$1.74\times {10}^6\mathrm{m}$and mass$7.35\times {10}^{22}\mathrm{kg}$?

Short answer

The acceleration due to gravity on the moon is $1.61\mathrm{m}/{\mathrm{s}}^2$.

Step-by-step solution

Step 1. Given Data

The radius of the moon is $r=1.74\times {10}^6\mathrm{m}$.

The mass of the moon is $m=7.35\times {10}^{22}\mathrm{kg}$.

Step 2. Understanding the gravitational acceleration

In this problem, the relation of acceleration due to gravity at any location on the planet’s surface will be utilized.

Step 3. Evaluating the gravitational acceleration on the moon

The relation of gravitational acceleration is given by,

$g=\frac{Gm}{r^2}$

Here, G is the gravitational constant.

On plugging the values in the above relation.

$\begin{array}{l}g=\left[\frac{\left(6.67\times {10}^{-11}\mathrm{N}·{\mathrm{m}}^2/{\mathrm{kg}}^2\right)\left(7.35\times {10}^{22}\mathrm{kg}\right)}{{\left(1.74\times {10}^6\mathrm{m}\right)}^2}\right]\\ g=1.61\mathrm{m}/{\mathrm{s}}^2\end{array}$

Thus, $g=1.61\mathrm{m}/{\mathrm{s}}^2$is the required acceleration due to gravity.