Question

In a physical balance working on the principle of moments, when 5 mg weight is placed on the left plan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?
A. Both the arms are of the same length.
B. Every object that is weighed using this balance appears lighter than its actual weight.
C. Left arm is longer than the right arm.
D. Left arm is shorter than the right arm.

Answer 1

Hint: For answering this question we need to have an idea about the point of application of force. The point of application of force gives us a relation between the clockwise and anticlockwise movements of a body which is required for attaining the balanced state. Once we have fulfilled the criteria of knowing what is the condition of a body for attaining balance, we can check each option as to whether they satisfy the condition or not. On the basis of that, we can find the right answer.

Complete step-by-step solution:
We know that the point of application of force is defined as a point at which if the net force is assumed to be acting then it will always produce the same effect of both the translation and the rotation.
For balance, we know that Anticlockwise moment = Clockwise moment.
So we can write this statement as:
$\text{Load }\!\!\times\!\!\text{ Load arm = Effect }\!\!\times\!\!\text{ Effort arm}$
So, if we try to represent this physical balance in a figure, it will be like,

Here, we can easily see that, ${{L}_{right}}>{{L}_{left}}$.
So, we can say that when 5mg weight is placed, the load arm will shift to the left side and hence the left arm becomes shorter than the right arm.
In option A, it is written that both the arms are of the same length which is also an incorrect option.
In option B, it is written that every object that is weighted using this balance appears lighter than its actual weight which is an incorrect option.
In option C, it is written that the left arm is longer than the right arm so this is an incorrect option.
In option D, it is written that the left arm is shorter than the right arm therefore this is the correct option.
So, the correct answer is Option D.

Note: The point of application as we know that is the exact location at which a force is applied on a body. This point is usually described by a set of coordinates which represent the body graphically by the tip of the arrowhead. The point of application for each force is unique in the case of a body.