Question

Assertion
The apparent weight of a body in an elevator moving with some downward
acceleration is less than the actual weight of a body.
Reason
The part of the weight is spent on producing downward acceleration, when body is
in the elevator.
A. Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Assertion and Reason are correct but Reason is not the correct explanation for Assertion.
C. Assertion is correct but Reason is incorrect.
D. Both Assertion and Reason are incorrect

Answer 1

Hint: We should know that acceleration is defined as the rate of change of the velocity. It is considered to be a vector quantity with the dimension as length divided by the square of time. The SI unit of the acceleration is given as metre per second square.

Complete step by step answer
We should know that let the mass of the body be m.
The diagram of the question is given below:

Therefore, the actual weight of the body in an elevator at the rest, ${\text{W = mg}}$
Now let the elevator move downward with an acceleration a.
Using the Newton’s law of motion: ${\text{ma = mg }} - {\text{ N} \ldots \ldots \ldots \ldots }\left( {\text{1}} \right)$
Thus, it seems that a part of weight is spent to produce the downward acceleration. Hence the reason statement is correct.
The equation (1) is given as: ${\text{N = mg - ma}}$
Thus, the apparent weight of the body is less than the actual weight of the body.
Hence the assertion statement is correct but reason is not the correct explanation of the assertion.

So, the correct answer is option B.

Note: We should know that Newton's first law of motion states that an object at rest remains at rest and an object is said to be in motion remains in the motion with the same velocity unless we act upon an unbalanced force on the object. This law is very important because there is almost everything that applies this law.
It should be known to us that the acceleration gives us an idea about the change in the velocity of an object over a specific increment of time. This results in the change in the object’s speed or the direction. The term constant or uniform acceleration is defined as the situation when the change in the velocity is constant over an equal period of time.