Stepwise Method for Accurate Volume Measurement
Lamina in Physics
Lamina in Latin is another word for leaf.
In physics, a lamina is a two-dimensional planar closed surface which has a mass and a surface density (its surface density is calculated in the units of mass per square area).
If the object has uniform density, the center of mass of a lamina is called its geometric center.
This geometric center is also called the geometric centroid of the object.
If you look at Fig.1, the center of mass of the lamina is P.
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We can see that the center of mass or the geometric centroid lies in the object itself.
What is a Screw Gauge?
Screw gauge is a form of the caliper that is used for measuring the thickness of thin glass and the diameter of a wire, plastic, or small dimensions of the objects like the sphere with an accuracy of 0.01 mm.
It was invented by William Gascoigne in the 17th Century, as an enhancement of the Vernier.
They are extensively utilized in the engineering field for obtaining accurate measurements.
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The Principle of a Screw Gauge
The screw gauge works on the principle of a screw in a nut and hence it is called a screw gauge.
A screw gauge works on the simple principle of converting small distances into larger ones by measuring the rotation of the screw.
This “screw” principle facilitates the reading of smaller distances on a scale after amplifying them. To simplify it further, let's take a normal screw with threads.
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To determine the volume of an irregular lamina using screw gauge
Irregular Lamina
An irregular lamina is an irregular polygon that doesn’t have a proper shape, and its thickness is negligible as compared to its length and breadth.
Its volume is calculated by the formula:
Volume = Area * Thickness
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The thickness of a lamina can be calculated by using the screw gauge while its surface area is measured using a graph paper.
Aim
To determine the volume of an irregular lamina
Materials Required:
Screw gauge
Irregular lamina of uniform thickness
A centimeter graph paper
A pencil
Theory
Screw gauge is also called the micrometer screw.
It uses a screw to amplify a very small movement so that it can be easily read.
It usually measures the diameters at 0.001 cm.
It consists of a U-shaped frame fitted with a screwed spindle that is attached to a thimble.
Parallel to the axis of the thimble, a scale graduated in mm is inscribed. This is known as the pitch scale.
The head of the screw consists of a ratchet that prevents undue tightening of the screw, and on the thimble, there is a circular scale known as the head scale that is divided into 50 to 100 equal parts.
A screw gauge works on the principle of the nut in a screw.
So, by rotating the screw head, we get the linear movement of the main scale which is a linear movement.
This linear movement is used to calculate the diameter of a wire or thickness of the metal plate.
This is how we can determine the volume of an irregular shaped lamina.
Here, we will talk about two parameters used in the screw gauge, that are:
1. The Pitch of a Screw Gauge
It is defined as the distance moved by the spindle per revolution that is measured by moving the head scale over the pitch scale to complete one full rotation. Its formula is given by:
Formula = Distance traveled by the screw/number of rotations made by the spindle
2. The Formula for Least Count of the Screw Gauge
The least count (LC) of the screw is defined as the distance traversed by the tip of the screw when turned through a division of the head scale.
Formula = Pitch of the screw gauge/total number of divisions on the circular scale.
Procedure to Determine the Volume of an Irregular Lamina
To calculate the thickness of an irregular lamina, use the procedure of finding the thickness of a wire.
To find the area of the lamina
Take a graph paper and consider the area of the square as 1 cm².
Place the lamina on a centimeter graph and mark its boundary using a pencil.
Count the number of squares enclosed on graph paper by the boundary of the lamina.
Let’s say, the counted squares are ‘n’ in total.
When multiplied by 1 cm², the area of the lamina becomes n cm².
Observations
Use the formula:
Area of the lamina = ____ cm² & the thickness = ____ cm.
Result
The volume of the lamina = ____ cm³.
FAQs on How to Measure the Volume of an Irregular Lamina Using a Screw Gauge
1. What is the overall procedure to measure the volume of an irregular lamina using a screw gauge?
Measuring the volume of an irregular lamina involves a two-step process. First, its surface area is determined using a graph paper. Second, its average thickness is measured precisely using a screw gauge. The volume is then calculated by multiplying the measured area and the average thickness.
2. What defines an object as an 'irregular lamina' in a Physics experiment?
An irregular lamina is essentially a flat, two-dimensional object whose outline does not follow a standard geometric shape like a circle or square. For experimental purposes, it is assumed to have a very small but nearly uniform thickness, which is negligible compared to its length and breadth but can be accurately measured with an instrument like a screw gauge.
3. How is the area of an irregular lamina calculated using graph paper?
To find the area, the following steps are taken:
- The lamina is placed on a centimetre graph paper and its boundary is traced with a sharp pencil.
- Count the number of complete squares (n₁) enclosed within the outline.
- Count the number of squares that are half or more than half-filled (n₂). Squares less than half-filled are ignored.
- The total area (A) is calculated as (n₁ + n₂) cm².
4. Why is it important to measure the lamina's thickness at several different points?
It is crucial to measure the thickness at multiple locations (e.g., 5-10 points) because the lamina may not be perfectly uniform. Taking several readings and calculating the mean (average) thickness helps to minimise random errors and provides a more accurate and representative value for the entire object, leading to a more reliable volume calculation.
5. Why is the screw gauge method preferred over the water displacement method for a lamina?
The water displacement method is unsuitable for a typical lamina for two main reasons. Firstly, a lamina is very thin, and immersing it in a measuring cylinder would displace a very small volume of water, which is difficult to read accurately. Secondly, if the lamina is made of a porous material like cardboard, it would absorb water, leading to an incorrect measurement. The screw gauge provides the necessary precision for measuring such small thicknesses.
6. How does a 'zero error' in the screw gauge affect the final result?
A zero error is a systematic error in the screw gauge that occurs when the zero of the circular scale does not align with the baseline of the main scale when the jaws are closed. If there is a positive zero error, the measured thickness will be higher than the actual value. If there is a negative zero error, the reading will be lower. This error must be identified and applied as a correction to each measurement to find the true thickness; otherwise, the calculated volume will be inaccurate.
7. What is the final formula used to calculate the volume of the irregular lamina in this experiment?
The final formula to determine the volume of the irregular lamina is:
Volume (V) = Area (A) × Average Thickness (t)
Here, 'A' is the surface area calculated from the graph paper (in cm²), and 't' is the mean (average) corrected thickness measured using the screw gauge (in cm). The final volume will be expressed in cubic centimetres (cm³).
