To Measure the Volume of an Irregular Lamina Using Screw Gauge

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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:

  1. Screw gauge

  2. Irregular lamina of uniform thickness

  3. A centimeter graph paper

  4. 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

  1. To calculate the thickness of an irregular lamina, use the procedure of finding the thickness of a wire.

  2. 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.

FAQ (Frequently Asked Questions)

Q1: What is an Irregular Object?

 Ans: An irregular object is a polygon that has different sides and angles.

Q2: How can we Find the Center of Mass of an Irregular Shaped Lamina?

Ans: Consider an irregular shaped lamina (Fig.a).

  1. Hang the lamina through at a point on the ceiling as shown in Fig.a.

  2. Attach a bob at the free end of the string. Here, this string makes a vertical line with the bob hanging at its free end.

  3. Now, hang the lamina through another point.

  4. Now, you have two lines drawn on the object which intersect each other.

  5. So, the center of the mass is the point of intersection of these two lines.

Q3: How can we Find the Area of Irregular Lamina?

Ans: The area of the lamina is equivalent to the sum total of the area of complete squares and the areas of squares half or more than half.

Let m be the total number of complete and more than half squares enclosed in the boundary of a lamina.

So, the calculated area will be in cm².

Q4: What is a Zero Error?

Ans: Any indication that the measuring device gives a false reading when the true reading of the quantity is zero.

For example, the reading of the ammeter turns to zero, when no current is flowing in the circuit. This error occurs because of systematic uncertainty in the device itself.