Question

The effect of rotation of the Earth on the value of acceleration due to gravity is

• A. Maximum at both poles
• B. Minimum at both poles
• C. Maximum at equator and minimum at the poles
• D. Minimum at the equator and maximum at the poles

Hint:

The variation of acceleration due to gravity due to the rotation of the earth is given by \(g^{'}=g-\omega ^{2} \, Rcos^{2} \theta\).

Answer 1

The Correct Option is C

The variation in acceleration due to gravity due to the rotation of the Earth is given as
 \(g^{'}=g-\omega ^{2} \, Rcos^{2} \theta\) , Where

• g' = Change in the acceleration due to gravity
• g= Acceleration due to gravity on the surface of the earth
• R = Radius of the earth
• \(\omega\) = Angular velocity of the earth
• \(\theta\) = Lattitude

(i) At poles,  \(\theta =90^{ \, }\)

 \(g_{p o l e}=g-\omega ^{2} \, Rcos^{2} 90^\circ =g-0\) 
\(g_{pole}=g\) 

There is no effect (minimum effect) of the rotation of the earth on acceleration due to gravity at the poles.

(ii) At equator, \(\theta =0^{ \, }\)

 \(g_{e q u a t o r}=g-\omega ^{2} \, Rcos^{2} 0^\circ\)
\(g_{equator}= \, g-\omega ^{2} \, R\) 

The effect of the rotation of the Earth on acceleration due to gravity is maximum at the equator.  The value of acceleration due to gravity is reduced by a factor of \(\omega^2R\) at the equator.

Discover More from Chapter: Gravitation

Answer 2

The correct Answer is (C): Maximum at equator and minimum at the poles

Real Life Applications

1. The length of a day: The day is longer at the equator than the poles due to the rotation of the earth. 
2. The shape of the Earth: The Earth is slightly flattened at the poles and bulges at the equator because the rotation of the earth creates centrifugal force which push the surface of the earth outward at the equator. 
3. The weight of objects: Due to the centrifugal force created by the rotation of the earth, the weight of the object is slightly less at the equator than the poles.

Question can also be asked as

1. How does the Earth's rotation affect the value of acceleration due to gravity? 
2. What is the centrifugal force, and how does it affect the value of acceleration due to gravity? 
3. What is the difference in acceleration due to gravity between the equator and the poles? 
4. How does the Earth's rotation affect the shape of the Earth?

Answer 3

The correct Answer is (C): Maximum at equator and minimum at the poles

The acceleration produced in the motion of the body under the effect of gravity of the earth is known as acceleration due to gravity.

Acceleration Due to Gravity on the Earth's Surface

• The acceleration due to gravity on the surface of the earth is given by \(g= \frac{GM_e}{R^2_e}\)
• On substituting the value of the Gravitational constant (G), Mass of the earth (M_e), and radius of the earth (R_e), we get the value of acceleration due to gravity on the surface of the earth as, g = 9.8 ms^-2

Acceleration Due to Gravity above the Earth's Surface

• The acceleration due to gravity above the surface of the earth at height h is given by \(g_h=\frac{GM_e}{(R_e+h)^2}\)
• If height h is much lesser than the radius of the earth i.e. \(h<<R_e\), then  \(g_h=g[1-\frac{2h}{R_e}]\)

Related Topics
Value of G	Gravity	Gravitational Force
Gravitation Formula	Difference between Gravitation and Gravity	Gravitation

Answer 4

As we know :
g' = g - ω²Rcos²λ
For poles at λ = 90° and the equator at λ = 0°
(a) For λ = 90
g'_pole = g - ω²Rcos²90° = g
g' = g
There is no effect on g at the poles.
(b) For λ = 0
g_equator = g - ω²Rcos²0°
= g - ω²R
The rotation of the Earth has the maximum effect on the value of g at the equator.
So, the correct option is (C) : Maximum at equator and minimum at the poles.