Question

Assertion and Reason are given in following questions. Each question have four option. One of them is correct it. (1) If both assertion and reason and the reason is the correct explanation of the Assertion. (2) If both assertion and reason are true but reason is not the correct explanation of the assertion. (3) If the assertion is true but reason is false. (4) If the assertion and reason both are false. Assertion: In the elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision. Reason: In the elastic collision the linear momentum of the system is conserved. (A)1 (B) 2 (C) 3 (D) 4

Short answer

Based on the analysis, both the assertion and the reason are true, and the reason is indeed the correct explanation for the assertion. Therefore, the correct answer is (A) 1.

Step-by-step solution

Analyze the assertion

We are given that in an elastic collision between two bodies, the relative speed of the bodies after the collision is equal to the relative speed before the collision. This is a property of elastic collisions and we recall that in an elastic collision, both linear momentum and kinetic energy are conserved.

Analyze the reason

The given reason states that in an elastic collision, the linear momentum of the system is conserved. This is a fundamental principle in physics called the conservation of linear momentum. For elastic collisions, not only linear momentum is conserved, but also the kinetic energy of the system.

Compare assertion and reason

Since both the assertion and reason are true statements regarding elastic collisions and linear momentum conservation, we now have to determine if the reason provided is the correct explanation for the assertion. In elastic collisions, due to both linear momentum and kinetic energy being conserved, it is possible to show mathematically that the relative speed of the objects after the collision is equal to the relative speed before the collision. The conservation of linear momentum is an important part of proving this. Therefore, the reason given is indeed the correct explanation for the assertion.

Choose the correct option

Based on our analysis in the previous steps, both the assertion and reason are true, and the reason is the correct explanation for the assertion. Therefore, the correct option is: (A) 1

Key concepts

Conservation of Linear Momentum

The conservation of linear momentum is a fundamental concept in physics, particularly crucial when analyzing collisions and interactions of objects. It states that the total linear momentum of a closed system remains constant, provided no external forces are acting on it. Momentum, a vector quantity, is the product of an object's mass and velocity. In a closed system, the sum of the momenta before any interaction must equal the sum after.

• Consider two colliding objects: the momentum of object 1 plus the momentum of object 2 before collision equals those after.
• This principle holds true for all types of collisions, such as elastic and inelastic.

In elastic collisions, specifically, the conservation of linear momentum is accompanied by the conservation of kinetic energy. This dual conservation leads to predictable outcomes, like maintaining relative speed, a unique aspect of elastic collisions.

Conservation of Kinetic Energy

In the context of collisions, kinetic energy plays a pivotal role in determining the type of interaction. Kinetic energy is the energy of motion, given by the formula \( KE = \frac{1}{2}mv^2 \), where \( m \) is mass and \( v \) is velocity. In an elastic collision, both momentum and kinetic energy are conserved, a rare but significant feature.

• Because both kinetic energy and momentum remain unchanged, the systems return to their original state of relativity post-collision.
• This conservation means the total kinetic energy pre- and post-collision is the same.

The conservation of kinetic energy ensures that the collision is neither "losing" energy to deformations or heat nor "gaining" from an external source—thereby perfectly elastic. This principle is often used in solving problems and verifying if a collision is elastic.

Assertion Reason Questions in Physics

Assertion Reason Questions are a popular format used in physics exams to test a student's understanding of concepts and relationships. This format presents a statement (assertion), followed by a related rationale (reason), and students must evaluate their validity and connection.

• The answer choices typically explore whether both statements are true and if the reason logically explains the assertion.
• Understanding fundamental principles, like conservation laws, is key to answering these questions correctly.

In the exercise given, the assertion states a property of elastic collisions, while the reason refers to a fundamental physical law. Recognizing the interconnection between conservation laws and collision outcomes allows students to accurately assess the rationale behind scientific phenomena.