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 will analyze the balance and apply the principle of moments. Here’s the step-by-step solution:
### Step 1: Understanding the Balance
A physical balance operates on the principle of moments, which states that for the beam to be in equilibrium, the moments about the pivot must be equal. The moment is calculated as the product of the force (weight) and the distance from the pivot.
### Step 2: Setting Up the Problem
Let:
- The weight placed on the left pan be \( W_L = 5 \, mg \) (where \( m \) is the mass and \( g \) is the acceleration due to gravity).
- The weight of the empty pan on the left be \( W_{pan} = mg \).
- The weight on the right pan be \( W_R = mg \) (the weight of the empty pan on the right).
### Step 3: Moment Calculation
When the beam is horizontal, the total moment on the left side must equal the total moment on the right side.
For the left pan:
- Total weight = \( 5mg + mg = 6mg \)
- Let the distance from the pivot to the left pan be \( d_1 \).
For the right pan:
- Total weight = \( mg \)
- Let the distance from the pivot to the right pan be \( d_2 \).
Setting the moments equal gives:
\[
(6mg) \cdot d_1 = (mg) \cdot d_2
\]
### Step 4: Simplifying the Equation
We can cancel \( mg \) from both sides of the equation (assuming \( mg \neq 0 \)):
\[
6d_1 = d_2
\]
### Step 5: Analyzing the Lengths
From the equation \( 6d_1 = d_2 \), we can see that:
\[
d_1 = \frac{d_2}{6}
\]
This indicates that \( d_1 \) (the distance to the left pan) is shorter than \( d_2 \) (the distance to the right pan).
### Conclusion
Since \( d_1 < d_2 \), we conclude that the left arm is shorter than the right arm.
### 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
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.
On fogy day two drivers spot in front of each other when 80 m apart, they were travelling 70 kmph and 60 kmph. Both apply brakes simultaneously which retards the car at the rate of 5 m//s^2 . Which of the following statement is correct?
A particle of mass m is moving along the x -axis with speed v when It collides with a particle of mass 2m initially at rest. After the collision, the first particle has come to rest and the second particle has split into two equal-mass pieces that are shown in the figure. Which of the following statements correctly describes the speeds of the two places? (thetagt0)
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 :
The two arms of a balanced are of unequal length. An object when placed in the left pan of the balance weighs 4 kg. The same object when placed in the right pan of the balance weighs 9 kg. The actual (or) true mass of the object is
A man weighing 60kg stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude 0.1m and frequency (2)/(pi) . its which of the following statement is correct ?
The periodicity is related to the electronic configuration. That is, all chemical and physical properties are a manifestation of the electronic configuration of the elements. The atomic and ionic radii generally decrease in a period from left to right. As a consequence, the ionization enthalpies generally increase and electron gain enthalpies become more negative across a period. In other words, the ionization enthalpy of the exterme left element in a period is the least and teh electron gain enthalpy of the element on the exterme right is the highest negative. This results into high chemical reactivity at the two extermes and the lowest in he centre. Similarly down the group, the increase in atomic and ionic radii result in gradual decrease in ionization enthalpies and a regular decrease (with exception in some third period elements) in electron gain enthalpies in the case of main group elements. The loss and gain of electrons can be co-related with the reducting and oxidising behaviour, and also with metallic and non-metallic character respectively, of the elements. Which of the following statements is correct?
We know that when two equal masses are placed on a line then, gravitational force on a third mass is zero due to these two masses when the third is placed at the centre of line joining the two masses. But if third mass is placed anywhere else on the x-axis, the gravitational force acts on that mass due to these two masses. Consider a system shown in figure. In this system two point masses of mass M each are placed at y-axis at a distance a from origin and these masses are fixed. If a third point mass of mass m is released at a distance x from origin on x-axis, then answer the following questions. If a >> x, then which of the following statements is correct about the motion of mass m ?