Question

Assertion and reason are given in following question. Each question have four options. One of them is correct select it. (A) Assertion is true. Reason is true and reason is correct explanation for Assertion. (B) Assertion is true. Reason is true but reason is not the correct explanation of assertion. (C) Assertion is true. Reason is false. (D) Assertion is false. Reason is true. Assertion: A body of mass $1 \mathrm{~kg}\( is moving with an acceleration of \)1 \mathrm{~ms}^{-1}$ The rate of change of its momentum is \(1 \mathrm{~N}\). Reason: The rate of change of momentum of body \(=\) force applied on the body. (A) a (B) \(\mathrm{b}\) (C) (D) \(\mathrm{d}\)

Short answer

(A)

Step-by-step solution

Write the assertion as a mathematical equation

We're given that a body of mass 1 kg is moving with an acceleration of 1 m/s². The rate of change of its momentum is given as 1 N (Newton). Recall that momentum (p) is defined as the mass (m) times the velocity (v) of a body, i.e., \(p=mv\). And the rate of change of momentum (Δp) would be the difference of momentum over the time interval (Δt), i.e., \(Δp = mΔv/Δt\). We can relate this to force (F) using Newton's second law of motion, which states that force is equal to mass times acceleration, i.e., \(F = ma\). From the given assertion, we have: Mass (m) = 1 kg, Acceleration (a) = 1 m/s², and Force (F) = 1 N. #Step 2: Analyze the reason#

Write the reason as a mathematical equation

The reason states that the rate of change of momentum of the body is equal to the force applied on the body. Mathematically, this relationship can be written as: \(Δp = F\). #Step 3: Check if the assertion is consistent with the reason#

Substitute the given values into the relationship

Since the assertion states that \(F=1\ N\) and the reason asserts that the rate of change of momentum (Δp) is equal to the force applied on the body, let's check whether the given values are consistent with the relationship: 1. First, use Newton's second law to find the force: \(F=ma\) -> \(F=(1\ \mathrm{kg})(1\mathrm{ms}^{-2}) = 1\ \mathrm{N}\). 2. Substitute the force value (F) into the relationship from the reason: \(Δp = F\) -> \(Δp = 1\ \mathrm{N}\). By comparing (1) and (2), we can see that both the assertion and the reason are true, and the reason is the correct explanation for the assertion. Therefore, the correct option is: (A) Assertion is true. Reason is true and reason is the correct explanation for Assertion.