Question

Define gravitational mass. The mass of the earth is $6\times {10}^{24}kg$ and that of the moon is $7.4\times {10}^{22}kg$. If the distance between the earth and the moon be $3.84\times {10}^{5}km$, calculate the force exerted by the earth on the moon. $(G=6.7\times {10}^{-11}N{m}^{2}k{g}^{-2})$
[3 MARKS]

Answer 1

Definition: 1 Mark
Problem: 2 Mark

1. The gravitational mass of the body is that property of an object which attracts another object by the gravitational force.
2. The force exerted by one body on another body is given by the Newton's formula:

$F=G\times \frac{m_1\times m_2}{r^2}$

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

Mass of the earth, $m_1=6\times {10}^{24}kg$

Mass of the moon, $m_2=7.4\times {10}^{22}kg$

And, Distance between the earth and moon, $r=3.84\times {10}^{5}km$

$=3.84\times {10}^5\times 1000m$

$=3.84\times {10}^{8}m$

Putting these values in the above formula, we get:

$F=\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}\times 7.4\times {10}^{22}}{(3.84\times {10}^8{)}^2}$

$F=2.01\times {10}^{20}N$

Thus, the gravitational force exerted by the earth on the moon is $2.01\times {10}^{20}N$. And this is an extremely large force. It is this extremely large gravitational force exerted by the earth on the moon which makes the moon revolve around the earth.