Problem 821 - JEE Physics

Question

Direction (Read the following questions and choose) (A) If both Assertion and Reason are true and the Reason is correct explanation of assertion (B) If both Assertion and Reason are true, but reason is not correct explanation of the Assertion (C) If Assertion is true, but the Reason is false (D) If Assertion is false, but the Reason is true Assertion: Even when orbit of a satellite is elliptical, its plane of rotation passes through the center of earth Reason: This is in accordance with the principle of conservation of angular momentum (a) \(\mathrm{A}\) (b) B (c) \(\mathrm{C}\) (d) \(\mathrm{D}\)

Step-by-Step Solution

Answer

The correct answer is (a) A, as both the assertion and reason are true, and the principle of conservation of angular momentum accurately explains why the plane of rotation of a satellite with an elliptical orbit passes through Earth's center.

Step 1: Understand Satellite's Orbit

The assertion claims that even if a satellite has an elliptical orbit, the plane of rotation of the satellite passes through the center of the Earth. This means that when a satellite orbits the Earth, its path always lies on a plane (2D surface) that passes through Earth's center. #Step 2: Understanding the Reason#

Step 2: Connect with the Principle of Conservation of Angular Momentum

The reason provided is the principle of conservation of angular momentum, which states that the angular momentum of a system remains constant if no external torques act on the system. It implies that if the satellite is not affected by external factors, its angular momentum will be conserved and should follow a certain trajectory or path in its orbit. #Step 3: Check if the Reason Conforms to the Assertion#

Step 3: Check for the Relation Between Angular Momentum and the Assertion

As the satellite orbits Earth, its path conforms to the conservation of angular momentum. According to this principle, the path of the satellite must be in a plane that passes through the center of the Earth. #Step 4: Determine the Correct Answer#

Step 4: Choose the Appropriate Option

Since both the assertion and reason are correct, and the principle of conservation of angular momentum accurately explains why the plane of rotation of a satellite with an elliptical orbit passes through Earth's center, we can opt for the correct answer: (a) A

Key Concepts

Satellite Orbit

A satellite orbit is the path that a satellite follows as it revolves around a celestial body, usually Earth. The orbit of a satellite is influenced by various factors such as gravity, velocity, and the shape of the path. Understanding the nature of satellite orbits is crucial for predicting their trajectories and maintaining communication and navigation systems.
When a satellite is launched, it achieves a velocity that allows it to balance the gravitational pull of the Earth, preventing it from falling back to the surface. This velocity is termed as orbital velocity, and it is what keeps the satellite in motion around Earth.

• If a satellite travels too slowly, it will fall back to Earth due to gravity.
• If it travels too quickly, it will escape into space.
• An optimal speed is crucial for maintaining a stable orbit.

The orbit of a satellite can take various shapes, such as circular or elliptical, and it is this path that dictates the satellite's functionality and coverage. In terms of communication and observation applications, understanding the satellite's trajectory helps ensure that it remains in the correct position over the right part of the Earth.

Elliptical Orbit

An elliptical orbit is one of the most common types of paths that a satellite follows when orbiting a celestial body like the Earth. Unlike a circular orbit that has a constant radius, an elliptical orbit is oval-shaped, meaning that the distance between the satellite and the object it orbits varies at different points in its path.
Elliptical orbits are governed by Kepler's Laws of Planetary Motion, which define how objects move in space. According to the first law, the orbit of a satellite around Earth is an ellipse, with Earth being at one of the two foci of this ellipse. This law indicates that at some points, the satellite may be closer to the Earth (perigee), while at other points, it may be farther away (apogee).

• An elliptical orbit can provide unique perspectives and extended coverage of certain areas on Earth during its closest approach.
• They allow satellites to have longer observation periods over a single area as they slow down at the apogee.
• The orbit is crucial for various applications including climate monitoring and reconnaissance.

Regarding the exercise, despite the elliptical nature of the orbit, the satellite's plane of rotation still passes through the center of the Earth, conforming to the principle of conservation of angular momentum.

Assertion and Reason Questions

Assertion and Reason questions are a common format used in education to test a student's understanding of scientific principles and their ability to logically connect cause and effect. In these exercises, you are presented with two statements: an assertion and a reason. Your task is to evaluate the truth of both statements and determine if the reason correctly explains the assertion.
To tackle these questions efficiently, it is essential to:

• Carefully analyze both the assertion and the reason separately.
• Understand the underlying scientific principles behind each statement.
• Determine if the reason logically supports the assertion.

In the provided exercise, the assertion is that even with an elliptical orbit, a satellite's plane of rotation passes through the Earth's center. The reason attributes this to the conservation of angular momentum. Understanding these concepts allows students to confidently identify the correct option, testing both their conceptual understanding and reasoning skills.