Answer
Verified
366.6k+ views
Hint: While solving the question one must be very careful to differentiate between acceleration due to gravity, $g$ and the Universal Gravitational constant, $G$. Newton’s Law of gravitation will further help to understand the concept of gravity and the formula involved in it.
Complete step by step solution:
It is a well-known fact that Sir Isaac Newton discovered gravity and formulated the law of gravitation. 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 the masses and inversely proportional to the square of the distance between them.” In mathematical form it can be written as:
$\begin{align}
& \,F\propto \dfrac{{{m}_{1}}\times {{m}_{2}}}{{{r}^{2}}} \\
& \Rightarrow F=G.\dfrac{{{m}_{1}}\times {{m}_{2}}}{{{r}^{2}}} \\
\end{align}$
Where
$F$ = Gravitational force in Newton
${{m}_{1}}$ and ${{m}_{2}}$ = masses of the bodies in kilograms
$r$ = distance between the masses in meters
$G$ = Gravitational constant
Here $G$ is a proportionality constant and the definition of constant is that its value never changes. So, be it earth, moon or any other planet, the value of $G$ will always be$6.67\times {{10}^{-11}}N.{{m}^{2}}.k{{g}^{-2}}$ .
On the other hand, when an object falls freely, its acceleration changes due to gravity. Such acceleration which is gained by the object due to gravitational force is called acceleration due to gravity, $g$. The formula for $g$ near the surface of the earth is given by:
$g=\dfrac{GM}{{{r}^{2}}}$
Where $g$ = acceleration due to gravity in $m/{{s}^{2}}$
$M$= mass of the earth
$r$ = radius of the earth
Therefore, acceleration due to gravity on the surface of the earth depends on the mass and radius of the earth. So, if the question asks about acceleration due to gravity on the moon, then it can be easily calculated if the mass and radius of the moon are known. Acceleration due to gravity also depends on the height of the object from the surface of the earth. When the height of the object increases from the surface of the earth, the value of $g$ decreases.
Note:
The acceleration due to gravity on the earth is $9.8m/{{s}^{2}}$ and on the moon is $\dfrac{1}{6}th$ that of earth. The value of $g$ differs for different altitudes and depths from the surface of the earth whereas $G$ is a physical constant that is invariant and does not depend on any factors whatsoever. Gravitational force is a weak force and hence the accuracy with which $G$ is measured is less.
Complete step by step solution:
It is a well-known fact that Sir Isaac Newton discovered gravity and formulated the law of gravitation. 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 the masses and inversely proportional to the square of the distance between them.” In mathematical form it can be written as:
$\begin{align}
& \,F\propto \dfrac{{{m}_{1}}\times {{m}_{2}}}{{{r}^{2}}} \\
& \Rightarrow F=G.\dfrac{{{m}_{1}}\times {{m}_{2}}}{{{r}^{2}}} \\
\end{align}$
Where
$F$ = Gravitational force in Newton
${{m}_{1}}$ and ${{m}_{2}}$ = masses of the bodies in kilograms
$r$ = distance between the masses in meters
$G$ = Gravitational constant
Here $G$ is a proportionality constant and the definition of constant is that its value never changes. So, be it earth, moon or any other planet, the value of $G$ will always be$6.67\times {{10}^{-11}}N.{{m}^{2}}.k{{g}^{-2}}$ .
On the other hand, when an object falls freely, its acceleration changes due to gravity. Such acceleration which is gained by the object due to gravitational force is called acceleration due to gravity, $g$. The formula for $g$ near the surface of the earth is given by:
$g=\dfrac{GM}{{{r}^{2}}}$
Where $g$ = acceleration due to gravity in $m/{{s}^{2}}$
$M$= mass of the earth
$r$ = radius of the earth
Therefore, acceleration due to gravity on the surface of the earth depends on the mass and radius of the earth. So, if the question asks about acceleration due to gravity on the moon, then it can be easily calculated if the mass and radius of the moon are known. Acceleration due to gravity also depends on the height of the object from the surface of the earth. When the height of the object increases from the surface of the earth, the value of $g$ decreases.
Note:
The acceleration due to gravity on the earth is $9.8m/{{s}^{2}}$ and on the moon is $\dfrac{1}{6}th$ that of earth. The value of $g$ differs for different altitudes and depths from the surface of the earth whereas $G$ is a physical constant that is invariant and does not depend on any factors whatsoever. Gravitational force is a weak force and hence the accuracy with which $G$ is measured is less.
Recently Updated Pages
Who among the following was the religious guru of class 7 social science CBSE
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Trending doubts
A rainbow has circular shape because A The earth is class 11 physics CBSE
Which are the Top 10 Largest Countries of the World?
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Who gave the slogan Jai Hind ALal Bahadur Shastri BJawaharlal class 11 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE