Question

The mass of the moon is 1% the mass of earth. The ratio of gravitational pull of earth on moon to that of moon on earth will be:
(A) 1:1
(B) 1:10
(C) 1:100
(D) 1:50

Answer 1

Hint:According to Newton’s law of gravitation: Everybody in the universe attracts every other body with a force which is directly proportional to the product of masses of two bodies and inversely proportional to the square of distance between their centers. Using this definition, find out the
gravitational force exerted by the two and you can eventually find out the required ratio.

Complete step by step answer:
Let ${m_1}$ and ${m_2}$ be the masses of the two bodies and $r$ be the distance between their
centers. Then gravitational force acting between them is,
$
F = \dfrac{{{m_1}{m_ 2}}}{{{r^2}}} \\
\Rightarrow F = G\dfrac{{{m_1}{m_2}}}{{{r^2}}} \\
$
where $G$ is a constant called universal gravitational constant.
Its value is, $G = 6.67 \times {10^{ - 11}}N{m^2}/k{g^2}$
When ${m_1} = {m_2} = 1$ and $r = 1$ then $F = G$ .

Thus universal gravitational constant is defined as the gravitational force acting between two bodies
of unit mass when both are separated by unit distance.Let mass of earth be ${M_E}$ , mass of moon be ${M_M}$ and $r$ be the distance between their centers. We are given that mass of moon is 1% of the mass of earth, so ${M_M} = \dfrac{{{M_E}}}{{100}}$.

Gravitational force exerted by earth on moon,
${F_{earth}} = G\dfrac{{{M_E}{M_M}}}{{{r^2}}} \\
\Rightarrow{F_{earth}} =G\dfrac{{{M_E} \times \dfrac{{{M_E}}}{{100}}}}{{{r^2}}} \\
\Rightarrow{F_{earth}} = G\dfrac{{{{({M_E})}^2}}}{{100{r^2}}}$
Gravitational force exerted by moon on earth,
${F_{moon}} = G\dfrac{{{M_M}{M_E}}}{{{r^2}}} \\
\Rightarrow{F_{moon}} =G\dfrac{{\dfrac{{{M_E}}}{{100}} \times {M_E}}}{{{r^2}}} \\
\Rightarrow {F_{moon}} = G\dfrac{{{{({M_E})}^2}}}{{100{r^2}}}$

The ratio of gravitational pull of earth on moon to that of moon on earth will be,
\[\dfrac{{{F_{earth}}}}{{{F_{moon}}}}=\dfrac{{G\dfrac{{{{({M_E})}^2}}}{{100{r^2}}}}}{{G\dfrac{{{{({M_E})}^2}}}{{100{r^2}}}}} \\
\therefore\dfrac{{{F_{earth}}}}{{{F_{moon}}}} = \dfrac{1}{1}\]
Thus ${F_{earth}}:{F_{moon}} = 1:1$

Hence, option (A) is the correct answer:

Additional Information:
Some evidences in support of existence of Gravitational force are –
1. Earth revolves around the sun and moon revolves around the earth because the necessary
centripetal force is provided by the gravitational force between them.
2. Everybody when released falls towards earth due to the gravitational force.
3. After the calculations based on gravitational force, artificial satellites are projected into space.

Note:
Body A and body B attract each other with an equal and opposite force, forming action and reaction
pair. Thus gravitational force obeys Newton’s third law of motion that is if a body exerts a force on
the other body then also exerts an equal and opposite force on it.