At which of the following place, weight of an object is maximum?
At poles
Understanding Weight and Gravity's Influence
The question asks where the weight of an object is maximum. To answer this, we need to understand what weight is and how it is affected by location on Earth.
What is Weight?
Weight is the force of gravity acting on an object's mass. It is given by the formula:
\[ W = m \times g \]
Where:
- \( W \) is the weight of the object.
- \( m \) is the mass of the object (which remains constant regardless of location).
- \( g \) is the acceleration due to gravity at that specific location.
Since mass \( m \) is constant, the weight \( W \) of an object depends directly on the value of the acceleration due to gravity \( g \). A higher value of \( g \) means a higher weight.
Variation of Acceleration Due to Gravity (\(g\)) on Earth
The acceleration due to gravity is not the same everywhere on Earth. This variation is primarily due to two main factors:
- Shape of the Earth: The Earth is not a perfect sphere; it is an oblate spheroid, meaning it is slightly flattened at the poles and bulges at the equator. This causes the radius of the Earth to be slightly smaller at the poles than at the equator. The acceleration due to gravity is inversely proportional to the square of the distance from the center of the Earth (\( g \propto 1/R^2 \)). Since the poles are closer to the Earth's center than the equator, gravity is stronger at the poles due to this factor.
- Rotation of the Earth: As the Earth rotates, objects on its surface experience a centrifugal force that acts outwards, away from the axis of rotation. This centrifugal force reduces the apparent acceleration due to gravity. The effect of this centrifugal force is maximum at the equator (where the speed of rotation is highest and the force acts directly opposite to gravity) and zero at the poles (which are on the axis of rotation).
Comparing \(g\) at Poles and Equator
- At the Poles: The radius is minimum, and the effect of Earth's rotation (centrifugal force) is zero. Both factors contribute to making \( g \) maximum at the poles.
- At the Equator: The radius is maximum, and the effect of Earth's rotation (centrifugal force) is maximum and opposes gravity. Both factors contribute to making \( g \) minimum at the equator.
- At other locations like the Tropic of Cancer, the value of \( g \) is between the values at the poles and the equator.
Therefore, the acceleration due to gravity \( g \) is highest at the poles.
Conclusion on Weight
Since \( W = m \times g \) and \( g \) is maximum at the poles, the weight of an object will be maximum at the poles.
Revision Table: Factors Affecting Gravity
| Factor | Effect on \(g\) | Impact at Poles | Impact at Equator |
|---|---|---|---|
| Shape of Earth (Distance from Center) | \( g \propto 1/R^2 \) | \( R \) is minimum, so \( g \) is higher | \( R \) is maximum, so \( g \) is lower |
| Rotation of Earth (Centrifugal Force) | Reduces apparent \(g\) | Effect is zero, no reduction in \(g\) | Effect is maximum, significant reduction in \(g\) |
Additional Information: Mass vs. Weight
It is important to distinguish between mass and weight:
- Mass: Mass is a fundamental property of an object that measures the amount of matter it contains. It is a scalar quantity and remains constant regardless of location or the presence of gravity. Mass is measured in kilograms (kg).
- Weight: Weight is the force exerted on an object due to gravity. It is a vector quantity and depends on both the object's mass and the local acceleration due to gravity. Weight is measured in Newtons (N).
So, while an object's mass stays the same whether it's at the poles or the equator, its weight will change because the force of gravity (\(g\)) changes.
Considering the variation in \(g\), the weight of an object is indeed maximum at the poles.
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:
When did Henry Cavendish report the measurement of the gravitational constant with the mass and density of the Earth?
