Question

Assertion (A): Newton’s laws can be applied to bigger bodies
Reason (R): During any kind of collision, the center of mass of the system is not accelerated.
A. Both Assertion and Reason are correct and the reason is the correct explanation
B. Both Assertion and Reason are correct but the reason does not give the correct explanation
C. Assertion is true but Reason is false
D. Assertion is false but Reason is true.

Answer 1

Hint: Before we get into answering the question, we have to understand the meaning of the term centre of mass.
The centre of mass is defined as the centre of a distribution of mass in space which has the property that the sum of weighted position vectors relative to this point is zero. Additionally, the centre of mass can be defined as the mean location of a distribution of mass in space.

Complete step by step answer:
Let us take a deeper look into these two statements to understand them better.

1. Assertion: Newton’s laws can be applied to bigger bodies
The contributions to Newton to the field of mechanics is exemplary. A whole new branch of science originated from his discoveries about motion, force and gravitation which was referred to as the classical mechanics, a subject that was developed over the seventeenth and eighteenth century.
However, in the early nineteenth century, there emerged a new branch of study based on the works of scientists like Schrodinger and Heisenberg, the mechanics of which could not be explained by the classical or Newtonian mechanics, known as Quantum Mechanics. Thus, for the first time, there came two different types of study in Mechanics – Classical and Quantum Mechanics.
The Quantum Mechanics were only applicable to microscopic objects meaning object's what size are in microns $\left( {{{10}^{ - 6}}m} \right)$
For all the objects whose size is greater than a micron, the laws of Newtonian classical mechanics continued to apply.
Hence, it is a true statement that Newton’s laws can be applied to bigger bodies, meaning the bodies whose size is greater than a micron.
So, the assertion is correct.

2. Reason: During any kind of collision, the centre of mass of the system is not accelerated.
The centre of mass is defined as the centre of a distribution of mass in space which has the property that the sum of weighted position vectors relative to this point is zero.
Also, the centre of mass can be defined as the point at which the entire mass of the object acts.
By Newton’s second law, we have that the force applied on a body is equal to the product of its mass and the acceleration.
$F = ma$
In other words, we can say that force is the rate of change of momentum of a body.
When a collision happens, there is no change in the momentum and hence, we can say the force is zero.
So, when $F = 0 \to a = 0$
This statement can be verified with Newton’s first law which states that as long as the force is applied on an object, the object continues to be in the state of rest or motion.
Other parts of the object might move in a collision but the centre of mass where the mass acts does not move when the force is zero.
Hence, it is true that during a collision, the centre of mass does not get accelerated.
So, the reason is correct.

Here, the assertion and reason both statements are correct, however, the fact that the centre of mass not accelerating in a collision has got to do with Newton’s laws of motion and not the fact that Newton’s law can be applied to bigger bodies.

Hence, the reason cannot be the right explanation for the assertion. Therefore, the correct option is Option B.

Note:
It is not always necessary that the centre of mass of a system of particles, necessarily be inside the dimensions of the body. For objects such as horseshoe and ring, the centre of mass remains at the vertical axis of these objects. This is the reason why you can spin them around your finger even though the body is not in contact with your finger because it provides perfect balance at that point.