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.

Key concepts

Momentum Change

Momentum is a fundamental concept in physics, directly tied to the motion of objects. Imagine pushing a shopping cart; the harder you push, the faster the cart moves. This observable effect is closely related to momentum. Mathematically, momentum (\(p\) ) is defined as the product of mass (\(m\) ) and velocity (\(v\) ), expressed as \(p = mv\).
The change in momentum over time describes how this momentum varies, potentially implying a force acting over time.

• Change in momentum: \(Δp = mΔv\).
• Force related to momentum change: \(F = \frac{Δp}{Δt}\).

In simple terms, the rate at which momentum changes equates to the force applied to the body. This helps explain how forces influence moving bodies. In our exercise, the rate of change of momentum is given as 1 N, which ties in with Newton's Second Law, asserting that a net force results in motion or a change in motion.

Force and Acceleration

Newton's Second Law of Motion is pivotal in understanding the relationship between force, mass, and acceleration. According to this law, the force applied to an object is equal to the mass of the object multiplied by its acceleration (\(F = ma\) ).
Imagine trying to push a car versus pushing a skateboard; you'll need much more force to accelerate the car because it's much heavier. Similarly, with a fixed force, a lighter object will accelerate more than a heavier one.

• Force (\(F\) ): Measured in Newtons (N), it's the push or pull on an object.
• Mass (\(m\) ): The amount of matter in an object, measured in kilograms (kg).
• Acceleration (\(a\) ): How quickly an object speeds up, measured in meters per second squared (m/s²).

In our problem, these variables are linked, demonstrating how a body with a certain mass and acceleration experiences a force that matches the rate of change of its momentum.

Assertion and Reason Questions

Assertion and reason questions test comprehension of theoretical statements and their underlying principles. You're given an assertion - a claimed fact - and a reason that supposedly explains it. The challenge lies in assessing the validity and connection between them.
In the example provided, the assertion claims that a 1 kg body's momentum changes at a rate of 1 N due to an acceleration of 1 m/s². The reason, stating that momentum change rate equals the applied force, serves as the explanation.

• Option A: Both assertion and reason are true, and reason is the correct explanation.
• Option B: Both are true, but reason does not explain the assertion.
• Option C: Assertion is true, reason is false.
• Option D: Assertion is false, reason is true.

The exercise's conclusion was that both statements were true, with the reason correctly clarifying the assertion, fitting Option A. This format sharpens analytical skills, teaching students to evaluate logic consistently.