Acceleration due to gravity is highest at ____.
the poles
Understanding Where Acceleration Due to Gravity is Highest
The acceleration due to gravity, often denoted by g, is the acceleration experienced by an object due to gravitational force. While we often use a standard value like 9.8 m/s², the actual value of g varies slightly across the Earth's surface. This variation depends on factors like altitude, latitude, and the Earth's shape and rotation.
Factors Influencing Acceleration Due to Gravity (g)
Several factors determine the value of g at different locations:
- Distance from the Earth's Center: According to Newton's Law of Universal Gravitation, the force of gravity is inversely proportional to the square of the distance between the centers of two masses. The formula for acceleration due to gravity at the surface is given by:
\[g = G \frac{M}{r^2}\]
where G is the universal gravitational constant, M is the mass of the Earth, and r is the radius of the Earth.
- Earth's Rotation: The Earth rotates on its axis, creating a centrifugal effect that acts outwards, opposing the gravitational force. This effect is maximum at the equator and zero at the poles. The effective acceleration due to gravity is reduced by this centrifugal force. The approximate formula accounting for rotation is:
\[g_{eff} \approx g - \omega^2 r \cos^2(\lambda)\]
where ω is the angular velocity of Earth's rotation, r is the radius at the given latitude, and λ is the latitude.
- Earth's Shape: The Earth is not a perfect sphere; it's an oblate spheroid, meaning it bulges at the equator and is flattened at the poles. This results in the radius being larger at the equator than at the poles.
Analysis of Options
Let's analyze why the acceleration due to gravity is highest at the poles:
1. The Poles
- Distance: Locations at the poles are closer to the Earth's center because the Earth is flattened there. A smaller radius (r) leads to a higher value of g according to the formula \(g \propto 1/r^2\).
- Rotation: The centrifugal effect due to Earth's rotation is zero at the poles (\(\cos(90^\circ) = 0\)). Therefore, there is no outward force counteracting gravity at the poles.
- Conclusion: Being closest to the center and experiencing no centrifugal effect results in the highest acceleration due to gravity at the poles.
2. At an Infinite Distance from the Earth
- As the distance from the Earth increases, the gravitational force decreases. At an infinite distance (\(r \to \infty\)), the acceleration due to gravity approaches zero.
3. The Equator
- Distance: The equator is farthest from the Earth's center due to the equatorial bulge. A larger radius (r) results in a lower value of g.
- Rotation: The centrifugal effect is maximum at the equator (\(\cos(0^\circ) = 1\)). This outward force significantly reduces the effective acceleration due to gravity.
- Conclusion: Due to the larger distance from the center and the maximum centrifugal effect, the acceleration due to gravity is lowest at the equator.
4. The Center of the Earth
- At the very center of the Earth, the gravitational forces from all parts of the Earth acting on an object cancel each other out. Effectively, there is no net gravitational pull towards the center, and the acceleration due to gravity is zero.
Summary
Based on the analysis of the factors influencing gravity (distance from the center and the effect of Earth's rotation), the acceleration due to gravity is strongest at the poles.
Similar Questions
The value of g on the moon is 1/6 th of the value of g on the earth. If a man can jump 1.5 m high on the earth, on the moon, he can jump up to a height of:
Fill in the blank with the most appropriate option.
The Universal Constant of Gravitation is ________.
Consider a hypothetical planet whose mass and radius are both half that of Earth. If g is the acceleration due to gravity on the surface of Earth, the acceleration due to gravity on the planet will be:
- Let \(W_e\) and \(W_m\) be the weight of an object on the Earth and the Moon, respectively. Then, the ratio \(W_e/W_m\) is equal to ______.
- A boy throws two balls in air in such a manner that when the first ball is at its maximum height he throws the second ball. If the balls are thrown with the time difference of one second, the maximum height attained by each ball is \((g = 10 \text{ m/s}^2)\)
- Two spheres of masses \(m\) and \(M\) are situated in air and the gravitational force between them is \(F\). The space between the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be:
- An object with a specific mass will weigh ______.
What will happen during the free fall of a massive object under the influence of gravitational force of the earth ?
Which of the following statements is/are INCORRECT?
A. The ratio of the force of gravitation between two masses, m1 and m2, kept at a distance R on the earth and on the moon is 1:1.
B. Nm2/kg2 is the SI unit of G.
C. The value of G depends on the distance between the bodies.
D. The value of G depends on the masses of the bodies.A 100 gram ball is kept on the top of a building of 70 m height. Find the potential energy of the ball (assume g = 10 m/s 2)
Important Questions from Gravity
Which of the following statement is correct?
I. Gravitation is a weak force unless large masses are involved.
II. The weight is equal to the product of mass and acceleration due to gravity.
What is the reason that the value of g (acceleration due to gravity) becomes greater at the poles than at the equator?
If the acceleration due to gravity on the surface of earth is g, then the acceleration due to gravity on the surface of a planet whose mass is same as that of earth and radius is twice as that of earth is ___________.
A man's mass is 72 kg on the earth. His mass on the moon will be:
At which of the following place, weight of an object is maximum?
