Question

A body weighs $25kg$ on the surface of the Earth. If the mass of the Earth is $6.0\times {10}^{24}kg$, the radius of the Earth is $6.4\times {10}^{6}m$ and the universal gravitational constant is $6.7\times {10}^{-11}N{m}^2/k{g}^2$, calculate the acceleration produced in the body?

Answer 1

Step 1: Given data

Mass of the body, $m=25kg$

Mass of the Earth, $M=6.0\times {10}^{24}kg$

Radius of the Earth, $R=6.4\times {10}^{6}m$

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 Earth

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

$$\begin{gathered} \Rightarrow F=\frac{6.7\times {10}^{-11}N{m}^2/k{g}^2\times 6.0\times {10}^{24}kg\times 25kg}{{(6.4\times {10}^{6}m)}^2} \\ \Rightarrow F=245.15N \end{gathered}$$

Step 3: Calculating the acceleration produced in the body

$\therefore$Acceleration produced in the body ,$a_{body}=\frac{Forceactingonthebody}{massofthebody}$

$\Rightarrow a_{body}=\frac{245.15N}{25kg}=9.81m{s}^{-2}$

Hence, the acceleration produced in the body is $9.81m{s}^{-2}$