Question

Calculate the mass of Earth. Given, the force that Earth exerts on a
mass (m) of 1 kg at its surface is 9.8 N. The radius of Earth ( R ) is
6. 4 × 106 m.

Answer 1

Answer:

6×10 to the power 24 the mass of earth

Answer 2

$\Huge\boxed{\underline {\underline {Answer}}}$

$\huge\sf{Given}$:-

Mass of object = 1 kg

Force that Earth exerts on a mass = 9.8 N

Radius of Earth = 6.4 × 10⁶ m

$\huge\sf{To\:Find }$:-

Mass of earth = ?

$\huge\sf{Formula \:used}$:-

$\large\boxed{Force = G\frac{m_{1}m_{2}}{{R}^{2}} }$

• $\mathrm{G = 6.67\times 10^{-11} N kg^{-2}m^{2}}$

$\huge\sf{Solution}$:-

Let:-

Mass of the object be $\bf{m_{1}}$.

Mass of the Earth be $\bf{m_{2}}$.

Now , according to the question we have:

$\sf{Force = G\frac{m_{1}m_{2}}{{R}^{2}}}$

$\implies 9.8 = 6.67 \times 10^{-11} \times \frac{1\times m_{2}}{6.4\times 10^{6}}^{2}$

$\implies m_{2} \approx 9.40 \times 10^{17}$