Question

A body weighs $1kg$on the surface of the Moon. If the mass of the Moon is $7.4\times {10}^{22}kg$, the radius of the Moon is $1740km$ and the gravitational constant is $6.7\times {10}^{-11}N{m}^2/k{g}^2$, calculate the acceleration produced in the Moon?

Answer 1

Step 1: Given data

Mass of the body, $m=1kg$

Mass of the Moon, $M=7.4\times {10}^{22}kg$

Radius of the Earth, $R=1740km=1.74\times {10}^{6}m$

Gravitational constant, $G=6.7\times {10}^{-11}N{m}^2/k{g}^2$

Step 2: Calculating the force acting upon the body and the Moon

$\therefore$Mutual force of attraction between the body and the Moon, $F=\frac{G\times M\times m}{R^2}$

$$\begin{gathered} \Rightarrow F=\frac{6.7\times {10}^{-11}N{m}^2/k{g}^2\times 7.4\times {10}^{22}kg\times 1kg}{{(1.74\times {10}^{6}m)}^2} \\ \Rightarrow F=1.63N \end{gathered}$$

Step 3: Calculating the acceleration produced in the Moon

$\therefore$Acceleration produced in the Moon ,$a_{moon}=\frac{ForceactingontheMoon}{massoftheMoon}$

$\Rightarrow a_{Moon}=\frac{1.63N}{7.4\times {10}^{22}kg}=2.20\times {10}^{-23}m{s}^{-2}$

Hence, the acceleration produced in the Moon is $2.20\times {10}^{-23}m{s}^{-2}$