Question

Compute the force of gravity on a body of mass $80kg$ lying on the surface of the earth. Given mass of the earth $6x{10}^{24}kg$, radius of the earth $6.4x{10}^{6}m$and $G=6.67X{10}^{-11}\frac{Nm²}{kg}$?

Answer 1

Step 1: Given :

Mass of the body $M=80kg$

Mass of earth $m_e=6\times 10²⁴kg$

Radius of Earth $R_e=6.4\times 10⁶m$

Value of $\text{'}G\text{'}=6.67\times 10⁻¹¹Nm²/kg²$

$F=$Force of gravity

$G=$ Universal Gravitational Constant

$M=$Mass of the body

$m_{e=}$ Mass of earth

$R_{e=}$ Radius of earth

Step 2: Formula used :

$F=\frac{GM{m}_e}{{R_e}^2}$

Step 3: By substituting values, we get :

$$\begin{gathered} \Rightarrow F=\frac{6.67\times {10}^{-11}\times 80\times 6\times {10}^{24}}{{(6.4\times {10}^6)}^2} \\ \Rightarrow F=\frac{6.67\times 80\times 6}{40.96}\times {10}^{24-23} \\ \Rightarrow F=78.164\times 10 \\ \Rightarrow F=781.64N \end{gathered}$$

Therefore, the force on the body is $F=781.64N$.