In a physical balance working on the principle of moments, when $5\,mg$ weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct ?

Question

A cylindrical tube $AB$ of length $l$, closed at both ends, contains an ideal gas of $1$ mol having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $AB$ and passing through the edge at end $A$, as shown in the figure. If $P_A$ and $P_B$ are the pressures at $A$ and $B$ respectively, then (consider the temperature to be same at all points in the tube)

Answer 1

To determine which statement is correct about the physical balance, we need to understand the principle of moments and how it applies to a balance beam.

The principle of moments states that for a beam to be balanced, the moment (or torque) on the left side must equal the moment on the right side. The moment is calculated as the product of the force (weight) and the distance from the pivot or fulcrum.
The balance becomes horizontal when the moments on both sides are equal. In this case, a weight of 5\,mg is placed on the left pan to make the beam horizontal, suggesting an imbalance in moments without it.
If the pans are of equal weight, we can deduce the imbalance must come from the lengths of the arms. The moment due to the weight on the left will be 5 \, mg \times L_{\text{left}}, where L_{\text{left}} is the length of the left arm.
Initially, there is no weight on the right pan, so for equilibrium, the left arm is naturally shorter. If the left arm were longer, or of equal length, there would be no need to add weight to achieve balance.

Given this understanding, the correct statement is:

Left arm is shorter than the right arm; because the left pan requires an additional weight to balance the beam, indicating the left arm is acting with less leverage than the right.

Thus, option "Left arm is shorter than the right arm" is the correct answer.

Answer 2

To determine which statement is correct about the physical balance, we need to understand the principle of moments and how it applies to a balance beam.

The principle of moments states that for a beam to be balanced, the moment (or torque) on the left side must equal the moment on the right side. The moment is calculated as the product of the force (weight) and the distance from the pivot or fulcrum.
The balance becomes horizontal when the moments on both sides are equal. In this case, a weight of 5\,mg is placed on the left pan to make the beam horizontal, suggesting an imbalance in moments without it.
If the pans are of equal weight, we can deduce the imbalance must come from the lengths of the arms. The moment due to the weight on the left will be 5 \, mg \times L_{\text{left}}, where L_{\text{left}} is the length of the left arm.
Initially, there is no weight on the right pan, so for equilibrium, the left arm is naturally shorter. If the left arm were longer, or of equal length, there would be no need to add weight to achieve balance.

Given this understanding, the correct statement is:

Left arm is shorter than the right arm; because the left pan requires an additional weight to balance the beam, indicating the left arm is acting with less leverage than the right.

Thus, option "Left arm is shorter than the right arm" is the correct answer.

In a physical balance working on the principle of moments, when $5\,mg$ weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct ?

The Correct Option is C

Solution and Explanation

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