Question

The acceleration due to gravity near the earth's surface is 9.8 m/s2, and the earth's radius is 6,400 km. From this data calculate the mass of the earth. Use any universal constant if required.

Answer 1

Answer:

Attached below.

Answer 2

Given:

• g = 9.8 m/s².
• Radius of earth = 6400 km

To find:

• Mass of earth ?

Calculation:

The gravitational acceleration on the surface of the earth will be given as :

$g = \dfrac{GM}{ {r}^{2} }$

• 'G' is Gravitational constant, 'M' is mass of earth and 'r' is radius of earth.

Now, putting the necessary values in SI UNITS:

$\implies M = \dfrac{g {r}^{2} }{ G }$

$\implies M = \dfrac{9.8 \times {(6400 \times {10}^{3} )}^{2} }{ 6.6 \times {10}^{ - 11} }$

$\implies M = \dfrac{9.8 \times 4096 \times {10}^{10} }{ 6.67 \times {10}^{ - 11} }$

$\implies M \approx 6.018 \times {10}^{24} \: kg$

So, mass of earth is approximately 6.018 × 10²⁴ kg.