Class 11 - To determine (a) Volume of Solid Cylinder and (b)Capacity of a Test Tube Using Vernier Callipers

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Class 11 Physics Practical | To find the volume of a solid cylinder and the capacity of a test tube using a Vernier Calipers

Lecture Overview & Video

Complete laboratory practical notes including apparatus, theory, formulas, filled observation tables, step-by-step calculations, and final results based on the tutorial by Talha's Physics Academy.

Source Video: Vernier Calipers Class 11 Physics Practicals | Sindh Board

1. Apparatus Required

• Vernier Calipers
• Solid Cylinder
• Test Tube

2. Least Count of Vernier Calipers

\(\text{Least Count (L.C.)} = \frac{\text{Smallest reading on main scale}}{\text{Total number of divisions on Vernier scale}} = \frac{0.1\text{ cm}}{20} = 0.005\text{ cm}\)

3. Theory & Working Formulas

Part A: Volume of a Solid Cylinder

The geometric volume of a solid cylinder is calculated using the formula:

\(V = \pi r^2 l = \pi \left(\frac{d}{2}\right)^2 l\)

Where \(l\) is the length of the cylinder, \(d\) is its diameter, and \(r\) is its radius (\(r = \frac{d}{2}\)).

Part B: Capacity of a Test Tube

The internal volume (capacity) of a test tube is given by:

\(\text{Capacity} = \pi R^2 D\)

Where \(D\) is the depth of the test tube measured using the depth strip, and \(R\) is its internal radius (\(R = \frac{d_{\text{internal}}}{2}\)).

4. Observations and Calculations

A. Measurement of Length of Solid Cylinder (\(l\))

Zero Error = 0 cm, Zero Correction = 0 cm

No. of Obs.	Main Scale Reading (\(M\)) [cm]	Vernier Coinciding Division (\(V.S.D.\)]	Fractional Part (\(V.S.D. \times L.C.\)) [cm]	Total Reading (\(X = M + \text{Fraction}\)) [cm]
1	3.3	13	0.065	3.365
2	3.3	14	0.070	3.370
3	3.3	15	0.075	3.375

Mean Length (\(l\)) = \(\frac{3.365 + 3.370 + 3.375}{3} = 3.370\text{ cm}\)

B. Measurement of Diameter of Solid Cylinder (\(d\))

No. of Obs.	Main Scale Reading (\(M\)) [cm]	Vernier Coinciding Division (\(V.S.D.\)]	Fractional Part [cm]	Total Reading (\(X\)) [cm]
1	0.9	11	0.055	0.955
2	0.9	12	0.060	0.960
3	0.9	12	0.060	0.960

Mean Diameter (\(d\)) = \(\frac{0.955 + 0.960 + 0.960}{3} = 0.958\text{ cm}\)

Radius of Cylinder (\(r\)) = \(\frac{d}{2} = \frac{0.958}{2} = 0.479\text{ cm}\)

C. Measurement of Depth of Test Tube (\(D\))

No. of Obs.	Main Scale Reading (\(M\)) [cm]	Vernier Coinciding Division (\(V.S.D.\)]	Fractional Part [cm]	Total Reading (\(X\)) [cm]
1	14.0	12	0.060	14.060
2	14.0	13	0.065	14.065
3	14.0	13	0.065	14.065

Mean Depth (\(D\)) = \(\frac{14.060 + 14.065 + 14.065}{3} = 14.063\text{ cm}\)

D. Measurement of Internal Diameter of Test Tube (\(d_{\text{internal}}\))

No. of Obs.	Main Scale Reading (\(M\)) [cm]	Vernier Coinciding Division (\(V.S.D.\)]	Fractional Part [cm]	Total Reading (\(X\)) [cm]
1	1.0	9	0.045	1.045
2	1.0	10	0.050	1.050
3	1.0	10	0.050	1.050

Mean Internal Diameter (\(d_{\text{internal}}\)) = \(\frac{1.045 + 1.050 + 1.050}{3} = 1.048\text{ cm}\)

Internal Radius (\(R\)) = \(\frac{d_{\text{internal}}}{2} = \frac{1.048}{2} = 0.524\text{ cm}\)

5. Calculations

1. Volume of Solid Cylinder (\(V\)):

\(V = \pi r^2 l = 3.14 \times (0.479)^2 \times 3.370 = 3.14 \times 0.2294 \times 3.370 = 2.427\text{ cm}^3\)

2. Capacity of Test Tube:

\(\text{Capacity} = \pi R^2 D = 3.14 \times (0.524)^2 \times 14.063 = 3.14 \times 0.2746 \times 14.063 = 12.124\text{ cm}^3\)

6. Results

• Volume of the given solid cylinder = \(2.427\text{ cm}^3\)
• Capacity of the given test tube = \(12.124\text{ cm}^3\)

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