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 ?
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 ?
A
Every object that is weighted using this balance appears lighter than its actual weight
B
Left arm is shorter than the right arm
C
Both the arms are of same length
D
Left arm is longer than the right arm
Text Solution
AI Generated Solution
The correct Answer is:
To solve the problem, we need to analyze the situation using the principle of moments (or torque). Here’s a step-by-step solution:
### Step 1: Understand the setup
We have a physical balance with two pans. When a 5 mg weight is placed on the left pan, the beam becomes horizontal. This indicates that the torques (moments) on both sides of the balance are equal.
### Step 2: Define the forces
Let:
- \( F_1 = 5 \, \text{mg} \) (the weight on the left pan)
- \( F_2 \) = weight of the empty pan on the right side (which is equal to the weight of the left pan since both pans are of equal mass).
### Step 3: Define the distances
Let:
- \( R_1 \) = distance from the pivot to the left pan
- \( R_2 \) = distance from the pivot to the right pan
### Step 4: Apply the principle of moments
According to the principle of moments, for the beam to be in equilibrium (horizontal position), the clockwise moments must equal the counterclockwise moments. Therefore, we can write:
\[
F_1 \cdot R_1 = F_2 \cdot R_2
\]
### Step 5: Analyze the situation
Since both pans are of equal mass, we can assume that \( F_2 \) is equal to the weight of the empty pan, which is less than \( F_1 \) (5 mg). Thus, we have:
\[
5 \, \text{mg} \cdot R_1 = F_2 \cdot R_2
\]
Given that \( F_1 > F_2 \), for the equation to hold true, \( R_1 \) must be less than \( R_2 \). This implies that the distance from the pivot to the left pan (where the 5 mg weight is) is shorter than the distance from the pivot to the right pan.
### Conclusion
Thus, we conclude that the left arm (distance \( R_1 \)) is shorter than the right arm (distance \( R_2 \)).
### Final Answer
The correct statement is: **The left arm is shorter than the right arm.**
---
Topper's Solved these Questions
Similar Questions
Explore conceptually related problems
At wood machine is attached below the left hand pan of a physical balance while equal weight (M+m) g is placed in the right hand pan. The beam is horizontal when the masses M and m on the left hand side are braked What will happen if the masses M and m are unbraked on the left hand side?
A faulty balance with unequal arms has its beam horizontal. Are the weights of the two pans equal ?
A ball of mass m is attached to a string whose other end is fixed. The system is free to rotate in vertical plane. When the ball swings, no work is done on the ball by the tension in the string. Which of the following statement is the correct explanation?
Two blocks of masses m_(1) and m_(2) are connected by an ideal sprit, of force constant k . The blocks are placed on smooth horizontal surface. A horizontal force F acts on the block m_(1) . Initially spring is relaxed, both the blocks are at rest. Which of the following statement is not true tn the watt of above system.
A body weighs 6gms when placed in one pan and 24gms when placed on the other pan of a false balance. If the beam is horizontal when both the pans are empty, the true weight of the body is :
When two solids are put in two pans of a beam balance, they exactly balance each other in air. When the two solids are completely immersed in water alongwith pans of balance, then they no longer balance each other. Which of the following is the incorrect statement about these balls?
When equal weights of O_(2) and N_(2) are placed in separate contaniners of equal volume at the same temerature which of the following statement is true ?
A man weighing 60kg stands on the horizontal platform of a spring balance. The plateform starts executing simple harmonic motion of amplitude 0.1m and frequency (2)/(pi) . its which of the following statement is correct ?
A body wights 8 g when placed on one pan and 18 g when placed on the other pan of a false balance .If the beam is horizontal when both the pans are empty the weght of the body is 4 xg Find value of x.