Question

The mass of the earth is $6 \times {10^{24}}Kg$ and that of the moon is $7.40 \times {10^{22}}Kg$ . The constant of gravitational force of attraction.
\left( A \right)38 \times {10^{18}} \\\ \left( B \right)20.2 \times {10^{19}} \\\ \left( C \right)7.60 \times {10^8} \\\ \left( D \right)1.90 \times {10^8} \\\

Answer 1

Hint : In order to solve this question, we are going to use the values of the masses of the moon and the earth that are given in the question, and the distance between the earth and moon and the gravitational constant are known values, so the force can be found using the Newton’s Gravitational law.
According to the Newton’s law of the gravitation, the gravitational force between two masses, ${m_1}$ and ${m_2}$ separated by a distance $d$ is
$F = \dfrac{{G{m_1}{m_2}}}{{{d^2}}}$
Where, $G$ is the gravitational constant.

Complete Step By Step Answer:
Let us solve this question by taking the given information in consideration:
It is given that the mass of the earth $\left( {{m_1}} \right)$ is $6 \times {10^{24}}Kg$ and
The mass of the moon $\left( {{m_2}} \right)$ is $7.40 \times {10^{22}}Kg$
The distance between the earth and the moon $\left( d \right)$ is $3.84 \times {10^5}Km$
Now, the value of the constant of gravitation $\left( G \right)$ is $6.7 \times {10^{ - 11}}N{m^2}K{g^{ - 1}}$
Now, the gravitational force using Newton’s law is given by $F = \dfrac{{G{m_1}{m_2}}}{{{d^2}}}$
Now to find the gravitational force between the earth and the moon is calculated by putting the values in the above formula
$F = \dfrac{{G{m_1}{m_2}}}{{{d^2}}} = \dfrac{{6.7 \times {{10}^{ - 11}}N{m^2}K{g^{ - 1}} \times 6 \times {{10}^{24}}Kg \times 7.40 \times {{10}^{22}}Kg}}{{{{\left( {3.84 \times {{10}^5}Km} \right)}^2}}} \\\ \Rightarrow F = \dfrac{{6.7 \times {{10}^{ - 11}}N{m^2}K{g^{ - 1}} \times 6 \times {{10}^{24}}Kg \times 7.40 \times {{10}^{22}}Kg}}{{{{\left( {3.84 \times {{10}^8}m} \right)}^2}}} \\\ \Rightarrow F = 20.17 \times {10^{19}}N$
Rounding off the value up to one decimal place, we get
$\Rightarrow F = 20.2 \times {10^{19}}N$
Hence, option $\left( B \right)20.2 \times {10^{19}}$ is correct.

Note :
It is important to check if all the values that are put in the formula are converted to the same scale of the units. The earth’s moon is the brightest object in our night sky. It appears so clear because it is very close to the Earth. The moon is a bit more than one - fourth the size of the earth and thus lesser mass. This is a much smaller ratio than other planets and their moons.