Chapter 4: Problem 533

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 : Linear momentum is conserved in both, elastic and inelastic collisions. Reason: Total energy is conserved in all such collisions. (A) 1 (B) 2 (C) 3 (D) 4

Short Answer

Expert verified

The correct option is (B) 2: "If both assertion and reason are true but reason is not the correct explanation of the assertion."

Step by step solution

To begin, we should clarify a few concepts: 1. Linear momentum is a measure of an object's motion and is calculated as the product of the object's mass and velocity. 2. In an elastic collision, both linear momentum and kinetic energy are conserved. 3. In an inelastic collision, linear momentum is conserved, but kinetic energy is not necessarily conserved. 4. Total energy is conserved in all systems, meaning that mechanical energy (kinetic plus potential energy) and any other forms of energy are conserved. With these concepts in mind, we can now analyze the assertion and reason. #Step 2#: Analyze the assertion

The assertion states that linear momentum is conserved in both elastic and inelastic collisions. Based on our understanding of these concepts, this assertion is true, as both elastic and inelastic collisions preserve linear momentum, even though kinetic energy conservation is different in each of them. #Step 3#: Analyze the reason

The reason claims that total energy is conserved in all such collisions (elastic and inelastic). This statement is true; however, it does not explain the reason why linear momentum is conserved in both types of collisions. Total energy is conserved, but this doesn't imply that linear momentum is also conserved because total energy includes various forms of energy, not limited to mechanical energy. So, the reason is true, but it does not account for the conservation of linear momentum in elastic and inelastic collisions. #Step 4#: Determine the relationship and choose the correct option

Based on our analysis, both the assertion and the reason are true, but the reason does not explain the conservation of linear momentum in both elastic and inelastic collisions. Therefore, the correct option is (B) 2: "If both assertion and reason are true but reason is not the correct explanation of the assertion."