Answer
Verified
39.3k+ views
Hint: Solution can be found by observing the gravitational attraction formula, where gravitational force is inversely proportional to the distance from the center of the earth. Thus, extending it to the concept that Earth is not a perfect sphere and the distance of poles and the equator is different from the center of earth.
Complete step-by-step answer:
Gravitational attractive force felt by a body on the earth’s surface is given as;
$\overset{\to }{\mathop{F}}\,=\dfrac{GMm}{{{r}^{2}}}$
G is the gravitational constant
r is the distance from the earth’s center
M is the mass of the earth
M is the mass of the body.
We can observe from the above image that earth is not a perfect sphere. It is slightly bulged at the equator, and flattened at the poles. Thus, from the above diagram we can observe that;
$R_e > R_p$
where, $R_e$ is the diameter at the equator, $R_p$ is the diameter at the poles
We know from the gravitational attraction and thus the acceleration due to gravity ‘g’ becomes:
$\begin{align}
& g=\dfrac{GM}{{{r}^{2}}} \\
& \Rightarrow g\propto \dfrac{1}{{{r}^{2}}} \\
\end{align}$
Thus, for poles:
${{g}_{p}}\propto \dfrac{1}{R_{p}^{2}}$
Thus, for equator:
${{g}_{p}}\propto \dfrac{1}{R_{e}^{2}}$
So, since ${{R}_{e}}>{{R}_{p}},{{g}_{e}}$ will be less than ${{g}_{p}}$. That is, gravitational force and the ‘g’ will be maximum at the poles.
Therefore, the correct answer to this question is option A. That is ‘g’ is maximum at poles.
Note: The gravitational force is an attractive force that is, it always attracts and never repels. It never pushes two masses further, only a pulling force is generated. The ‘g’ is the acceleration of gravity and is equal to $9.8m/{{s}^{2}}$ at Earth surface, i.e., at sea level.
Complete step-by-step answer:
Gravitational attractive force felt by a body on the earth’s surface is given as;
$\overset{\to }{\mathop{F}}\,=\dfrac{GMm}{{{r}^{2}}}$
G is the gravitational constant
r is the distance from the earth’s center
M is the mass of the earth
M is the mass of the body.
We can observe from the above image that earth is not a perfect sphere. It is slightly bulged at the equator, and flattened at the poles. Thus, from the above diagram we can observe that;
$R_e > R_p$
where, $R_e$ is the diameter at the equator, $R_p$ is the diameter at the poles
We know from the gravitational attraction and thus the acceleration due to gravity ‘g’ becomes:
$\begin{align}
& g=\dfrac{GM}{{{r}^{2}}} \\
& \Rightarrow g\propto \dfrac{1}{{{r}^{2}}} \\
\end{align}$
Thus, for poles:
${{g}_{p}}\propto \dfrac{1}{R_{p}^{2}}$
Thus, for equator:
${{g}_{p}}\propto \dfrac{1}{R_{e}^{2}}$
So, since ${{R}_{e}}>{{R}_{p}},{{g}_{e}}$ will be less than ${{g}_{p}}$. That is, gravitational force and the ‘g’ will be maximum at the poles.
Therefore, the correct answer to this question is option A. That is ‘g’ is maximum at poles.
Note: The gravitational force is an attractive force that is, it always attracts and never repels. It never pushes two masses further, only a pulling force is generated. The ‘g’ is the acceleration of gravity and is equal to $9.8m/{{s}^{2}}$ at Earth surface, i.e., at sea level.
Recently Updated Pages
silver wire has diameter 04mm and resistivity 16 times class 12 physics JEE_Main
A parallel plate capacitor has a capacitance C When class 12 physics JEE_Main
A series combination of n1 capacitors each of value class 12 physics JEE_Main
Which of the following is not true in the case of motion class 12 physics JEE_Main
The length of a potentiometer wire is 10m The distance class 12 physics JEE_MAIN
Ratio of magnetic intensities for an axial point and class 12 physics JEE_Main
Other Pages
A motorcycle is going on an over bridge of radius R class 11 physics JEE_Main
Formula for number of images formed by two plane mirrors class 12 physics JEE_Main
The mole fraction of the solute in a 1 molal aqueous class 11 chemistry JEE_Main
Explain the construction and working of a GeigerMuller class 12 physics JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
A closed organ pipe and an open organ pipe are tuned class 11 physics JEE_Main