Problem 49 - Master Resource Book in JEE Main Physics

Question

Assertion There is no effect of rotation of earth on acceleration due to gravity at poles. Reason Rotation of earth is about polar axis.

Step-by-Step Solution

Answer

Assertion is true and the reason correctly explains why.

Step 1: Understanding the Context

The exercise involves understanding the assertion and the reason provided. The assertion claims that Earth's rotation does not affect the acceleration due to gravity at the poles. The reason given is because Earth's rotation takes place around the polar axis.

Step 2: Analyzing the Assertion

The assertion states that the rotation of Earth has no effect on the acceleration due to gravity at the poles. At the poles, any centrifugal force due to rotation is negligible because the poles are located on the axis of rotation.

Step 3: Examining the Reason

The reason asserts that Earth's rotation occurs about the polar axis. This means that the effects of centrifugal force caused by rotation are not applicable at the poles as there is no lateral displacement from the axis of rotation.

Step 4: Evaluating the Relationship

Assess whether the reason justifies the assertion. The reason correctly supports the assertion because the rotational effect, specifically centrifugal force, is zero at the poles as the poles coincide with the axis of rotation. Hence, the rotation of Earth indeed has no effect on gravity at the poles.

Key Concepts

Centrifugal Force

Centrifugal force plays a significant role in understanding how Earth's rotation influences gravity. As the Earth spins, it creates an outward force known as the centrifugal force, which affects objects on its surface, primarily at the equator. This force is due to Earth's rotation and acts perpendicular to the axis of rotation.

• This force is strongest at the equator because it is furthest from the axis of rotation, resulting in a slight reduction in the gravitational force experienced there.
• As you get closer to the poles, the centrifugal force diminishes because the surface velocity of rotation decreases.
• At the poles, the centrifugal force is essentially nonexistent, meaning the gravitational force isn't reduced by Earth's rotation.

Understanding how centrifugal force varies with latitude helps clarify why gravity's acceleration is unaffected at the poles. At any point away from the axis, the centrifugal force attempts to "throw" objects outward, counteracting some of gravitational pull. However, this is negligible at the poles due to zero lateral displacement from the axis.

Poles of Earth

The poles of Earth, the North and South Poles, are unique points where the axis of rotation intersects Earth's surface. These poles are crucial to understanding gravity's uninterrupted pull in those regions.

• The poles are fixed and do not move laterally due to Earth's rotation.
• This stationary position means there is no centrifugal force acting on objects at the poles, allowing for a pure gravitational force to act.
• As a result, the gravitational acceleration is greater at the poles compared to the equator, where centrifugal force slightly counteracts gravity.

When considering why gravity is unaffected by rotation at the poles, it is key to recognize that the poles align perfectly with the axis of rotation. This removes any lateral movement and the resultant centrifugal force that could interfere with the gravitational pull experienced at other latitudes.

Axis of Rotation

The axis of rotation is an imaginary line extending through Earth from the North Pole to the South Pole, around which the planet rotates. This concept is central to understanding the lack of centrifugal influence on gravity at the poles.

• Earth's rotation around the axis is what gives us day and night.
• Objects at the equator experience a greater centrifugal force since they are further from this axis.
• However, any point directly on this axis, such as the poles, does not move laterally, therefore experiencing no centrifugal force.

The lack of lateral movement at the poles, due to their position on the axis of rotation, ensures that only gravity influences objects at these locations. Thus, when examining how Earth's rotation impacts gravity, it's pivotal to consider the role of the axis, as it determines how centrifugal forces are distributed across the planet's surface. By being directly on the axis, the poles become regions where Earth's rotation does not alter gravitational forces.