While calculating the correction to volume, V=(1+3e)v', e can calculated by:
ΔL / L
Correction to Volume Calculation
The question provides a formula for calculating the corrected volume, $V$, based on a measured volume, $v'$, and a factor related to expansion, $e$. The formula is given as:
$$V = (1+3e)v'$$
Here, $V$ represents the corrected volume, $v'$ is the measured volume (or initial volume), and $e$ is a quantity related to the linear change or strain in the material.
In many physical contexts, especially when dealing with changes in dimensions due to factors like temperature or stress, a small change in length is related to the original length. The ratio of the change in length ($\Delta L$) to the original length ($L$) is often referred to as linear strain or proportional change in length. It is a fundamental measure of how much a material deforms relative to its original size.
The relationship between volume change and linear change for small expansions is approximately given by relating the volumetric strain to the linear strain. If a material undergoes a small linear strain $e$ along each dimension, the volumetric strain is approximately $3e$. In the given formula $V = (1+3e)v'$, the term $3e$ represents the fractional change in volume, meaning $\frac{V - v'}{v'} = 3e$. This implies that $e$ is related to the linear fractional change.
The quantity $e$ in this formula is defined as the linear strain or the relative change in length. This is calculated by dividing the change in length ($\Delta L$) by the original length ($L$).
Therefore, the formula for $e$ is:
$$e = \frac{\Delta L}{L}$$
Now let's look at the given options to find the one that matches this definition of $e$.
- Option 1: $(\Delta L - L) / L$. This is not the standard definition of linear strain.
- Option 2: $L / \Delta L$. This is the reciprocal of the linear strain.
- Option 3: $\Delta L / L$. This matches the definition of linear strain.
- Option 4: $L - \Delta L$. This is the absolute change in length subtracted from the original length, which is not a strain or relative change.
Based on the relationship between volume correction and linear expansion, $e$ is calculated as the ratio of the change in length to the original length.
Thus, $e$ can be calculated by the formula $\frac{\Delta L}{L}$.
Important Questions from Accuracy and Errors
Consider the following statements.
A. Cumulative errors are more important than compensating errors
B. All cumulative errors are equally important
C. The more times a line is measured, the more likely the accidental errors to disappear from mean
D. Variation in temperature results in compensating error
Which of the above statements is/are correct?
An angle measured with theodolite is α with weight 2. The weight of \(\rm \frac{\alpha}{4}\) will be
Which of these is not a cumulative error while surveying?
Incorrect counting of tape lengths in chaining is ________.
According to the theory of probability, small errors tend to be more frequent than the large ones. This means they are more ________.
