Newton's Law Of Gravitation - Practice Questions & MCQ

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Newton's law of Gravitation is considered one of the most asked concept.
39 Questions around this concept.

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An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth’s surface. The radius of the earth is R, while its mass is M. The gravitational pull F_G on the astronaut is :

Zero since astronaut feels weightless

$0< F_{G}< \frac{GMm}{R^{2}}$

$\frac{GMm}{\left ( R+h \right )^{2}}< F_{G}< \frac{GMm}{R^{2}}$

$F_{G}= \frac{GMm}{\left ( R+h \right )^{2}}$

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Suppose the gravitational force varies inversely as the n^th power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to :

$R^{\left ( \frac{n+1}{2} \right )}$

$R^{\left ( \frac{n-1}{2} \right )}$

$R^{n}$

$R^{\left ( \frac{n-2}{2} \right )}$

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Concepts Covered - 1

Newton's law of Gravitation

According to Newton's law of gravitation, the gravitational force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Due to gravitational force, Each particle in this universe attracts every other particle.

The direction of this force is along the line joining the particles.

Let two particles of masses $m_1$ and $m_2$ separated by a distance r exert a Force F on each other

And Magnitude of F is given as

$F\; \alpha\; \frac{m_{1}m_{2}}{r^{2}}$

Or, $F\; = \frac{G\, m_{1}\, m_{2}}{r^{2}}$

Where

$F\rightarrow$ Force

$G\rightarrow$ Gravitational constant

$m_1,m_2\rightarrow$ Masses

$r\rightarrow$ Distance between masses

The vector form of formula

According to Newton's law of gravitation

$\vec{F}_{12}=\frac{-Gm_1m_2}{r^{2}}(\hat{r}_{21})$

Or $\vec{F}_{12}=\frac{-Gm_1m_2}{r^{3}}(\vec{r}_{21})$

Where $\hat{r}_{21}\rightarrow$ Position vector

Here negative sign indicates that the direction of $\vec{F}_{12}$ is opposite to that of $\vec{r}_{21}$

And $\hat{r}_{12}=-\hat{r}_{21}$

So, $\vec{F}_{12}=-\vec{F}_{21}$

Means Gravitational force between two bodies form an action and reaction pair.

i.e. the forces are equal in magnitude but opposite in direction.

This is in accordance with Newton's third law of motion

Universal Gravitational Constant (G)

If $m_1=m_2=1 \ kg$ and r=1 m then F=G

I.e Universal gravitational constant is equal to the Gravitational force between two bodies each having unit mass and their centers are placed unit distance apart.

Value of G is $6.67\times 10^{-11}\; N\: -m^{2}kg^{-2}\; \; \; (S.I.)$

Its Dimension Formula is $\left [ M^{-1}L^{3}T^{-2} \right ]$

Value of G does not depend upon the nature & size of bodies

Also, it is also independent of the nature of medium between two bodies.

Properties of Gravitational Force

Always attractive
It is the central force
Weakest force (Ratio of $F_{g}\; \; to \; \; F_{e}$ between two electrons is $10^{-43}$ )
It is a conservative force
It is independent of the medium between the particles.
Gravitational force is long range-force.
Principle of superposition is valid for Gravitational Force