Question

Assertion: The apparent weight of a body in an elevator moving with some downward acceleration is less then the actual weight of body.

Reason: The part of the weight is spent in producing downward acceleration, when body is in elevator.

• A. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
• B. If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
• C. If Assertion is true but Reason is false.
• D. If the Assertion and Reason both are false.
• E. If Assertion is false but Reason is true.

Answer 1

The correct option is A

If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.

Let the mass of the body be $m$.

The diagram for the situation is

The actual weight of the body in downward direction is $mg$ and the normal force acting on upward direction is $N$.

The net force acting on body is

$$\begin{gathered} F_{net}=mg-N \\ N=mg-F_{net} \\ N=mg-ma \end{gathered}$$

Explanation for Assertion statement:

1. The actual weight of the body in an elevator at the rest, $W=mg$
2. The apparent weight of a body in an elevator moving with downward acceleration $a$ is given by $N=m(g–a)$.
3. Thus, the apparent weight of the body is less than the actual weight of the body.

Explanation for Reason statement:

1. When the elevator moves downward with an acceleration $a$.
2. It seems that a part of the weight is spent to produce the downward acceleration.
3. Hence the reason statement is correct.

The apparent weight of a body in an elevator moving with some downward acceleration is less then the actual weight of body as the part of weight is spent to produce downward acceleration.

Therefore, both Assertion and Reason are true and the reason is the correct explanation of the Assertion.

Hence, option A is correct.