Class 11 Physics Notes Chapter 9 (Chapter 9) – Lab Manual (English) Book

Detailed Notes with MCQs of Chapter 9 from your Physics Lab Manual. This experiment is crucial, not just for your practical exams but also because the concepts of elasticity, stress, and strain frequently appear in various government entrance exams. Pay close attention as we break down the determination of Young's Modulus for a given wire.

Chapter 9: To determine the Young's modulus of elasticity of the material of a given wire.

1. Aim:
To find the Young's modulus (Y) of the material of a given metallic wire using Searle's apparatus.

2. Apparatus:

• Searle's apparatus (consisting of two identical metal frames connected by a spirit level or pointer attached to a micrometer screw, suspended by two identical wires - one experimental, one reference/compensating).
• Experimental wire (whose Young's modulus is to be determined).
• Reference/Compensating wire (made of the same material and dimensions as the experimental wire).
• Slotted weights (usually 0.5 kg each) and a hanger.
• Metre scale (for measuring the original length of the wire).
• Screw gauge (for measuring the diameter/radius of the wire).
• Spirit level.

3. Theory:

• Elasticity: The property of a material by virtue of which it regains its original shape and size after the removal of deforming forces.

• Stress: The internal restoring force set up per unit area of cross-section of a deformed body.

  • Longitudinal Stress = Force (F) / Area (A) = Mg / (πr²)
  • Unit: N/m² or Pascal (Pa)
  • Dimension: [ML⁻¹T⁻²]

• Strain: The ratio of the change in dimension to the original dimension.

  • Longitudinal Strain = Change in length (l) / Original length (L)
  • Unit: Dimensionless
  • Dimension: [M⁰L⁰T⁰]

• Hooke's Law: Within the elastic limit, stress is directly proportional to strain.

  • Stress ∝ Strain
  • Stress = Y × Strain

• Young's Modulus (Y): It is the ratio of longitudinal stress to longitudinal strain, within the elastic limit. It measures the stiffness of the material.

  • Y = Longitudinal Stress / Longitudinal Strain
  • Formula: Y = (F/A) / (l/L) = (Mg / πr²) / (l/L) = (MgL) / (πr²l)
  • Where:
    • M = Mass suspended (load applied)
    • g = Acceleration due to gravity (approx. 9.8 m/s²)
    • L = Original length of the experimental wire
    • r = Radius of the experimental wire (measured using screw gauge, r = diameter/2)
    • l = Extension (increase in length) of the wire corresponding to mass M
  • Unit: N/m² or Pascal (Pa) (Same as Stress)
  • Dimension: [ML⁻¹T⁻²] (Same as Stress)

• Searle's Apparatus:

  • It uses two wires (experimental and reference) to compensate for any yielding of the support and thermal expansion/contraction due to temperature changes during the experiment. Both wires experience similar temperature changes, so the relative extension measured is only due to the applied load.
  • A spirit level and micrometer screw arrangement allow for precise measurement of the small extension (l).

4. Procedure Outline:

1. Setup: Suspend the Searle's apparatus from a rigid support. Attach the experimental and reference wires. Ensure the wires are straight and free from kinks.
2. Measure Original Length (L): Measure the length of the experimental wire from the point of suspension to the point where it's attached to the frame, using a metre scale.
3. Measure Diameter (d) / Radius (r): Measure the diameter of the experimental wire at several points (at least 5) along its length and in two mutually perpendicular directions at each point using a screw gauge. Calculate the mean diameter (d) and then the mean radius (r = d/2). Calculate the cross-sectional area A = πr².
4. Initial Setup: Apply a dead load (initial weight, e.g., 1 kg) to both wires to keep them taut. Note the reading on the micrometer screw when the spirit level bubble is exactly in the centre. This is the initial reading.
5. Loading: Gradually increase the load on the experimental wire hanger in steps (e.g., 0.5 kg increments). For each load, wait for a minute or two for the wire to extend fully and stabilize. Adjust the micrometer screw to bring the spirit level bubble back to the centre and record the micrometer reading.
6. Unloading: After reaching the maximum desired load (well within the elastic limit), gradually decrease the load in the same steps. Again, record the micrometer reading for each load after stabilizing and bringing the bubble to the centre.
7. Calculate Extension (l): Find the mean micrometer reading for each load (average of loading and unloading readings). The extension (l) for a given added mass (M) is the difference between the mean reading for that load and the initial reading (with the dead load only).
8. Calculations: Calculate Y using the formula Y = (MgL) / (πr²l) for each load added (beyond the dead load). Find the average value of Y.
9. Graphical Method (Optional but Recommended): Plot a graph between the applied load (M or Mg) on the Y-axis and the corresponding mean extension (l) on the X-axis. The graph should be a straight line passing through the origin (or close to it). Calculate the slope of this line: Slope = M/l (or Mg/l).
   • If slope = M/l, then Y = (Slope × g × L) / (πr²)
   • If slope = Mg/l, then Y = (Slope × L) / (πr²)

5. Precautions:

1. The support must be rigid.
2. Wires should be of the same material, length, and diameter (especially for the reference wire).
3. Remove kinks from the wire before starting. Apply a dead load to keep the wire taut.
4. Measure the diameter of the wire accurately using a screw gauge at multiple points and directions.
5. Add and remove weights gently to avoid jerks.
6. Wait for stabilization before taking readings.
7. Take readings during both loading and unloading to minimize errors due to elastic after-effect.
8. The load applied should not exceed the elastic limit of the wire material.
9. Read the micrometer screw carefully, avoiding parallax error and checking for backlash error (by always moving the screw in the same direction when taking a reading).
10. Use a long wire so that the extension is measurable.

6. Sources of Error:

1. Kinks in the wire.
2. Backlash error in the screw gauge or the micrometer of Searle's apparatus.
3. Errors in measurement of L, r, and l.
4. Non-uniformity of the wire's cross-section.
5. Yielding of the support (largely compensated by the reference wire).
6. Temperature changes during the experiment (largely compensated).
7. Exceeding the elastic limit.

Multiple Choice Questions (MCQs)

Here are 10 MCQs based on this experiment for your practice:

1. Young's modulus (Y) is defined as the ratio of:
a) Longitudinal Stress to Lateral Strain
b) Longitudinal Stress to Longitudinal Strain
c) Shear Stress to Shear Strain
d) Bulk Stress to Bulk Strain

2. The SI unit of Young's modulus is:
a) N/m
b) N/m²
c) N-m
d) Dimensionless

3. In the experiment to determine Young's modulus using Searle's apparatus, the purpose of the reference wire is primarily to:
a) Support the apparatus frame
b) Measure the extension accurately
c) Compensate for thermal expansion and yielding of the support
d) Double the measured extension

4. Which instrument is used to measure the diameter of the experimental wire accurately?
a) Metre scale
b) Vernier callipers
c) Spherometer
d) Screw gauge

5. According to Hooke's Law, within the elastic limit:
a) Strain is directly proportional to Stress
b) Stress is directly proportional to Strain
c) Stress is inversely proportional to Strain
d) Stress is independent of Strain

6. If the length of a wire is doubled and its radius is halved, its Young's modulus will:
a) Become four times
b) Become half
c) Remain unchanged
d) Become one-fourth

7. In the formula Y = (MgL) / (πr²l), 'l' represents:
a) Original length of the wire
b) Total length after extension
c) Radius of the wire
d) Extension produced by mass M

8. To get a larger measurable extension for a given load, the experimental wire should ideally be:
a) Short and thick
b) Long and thick
c) Short and thin
d) Long and thin

9. A graph is plotted between the load (Mg) applied (Y-axis) and the extension (l) produced (X-axis). The slope of this graph represents:
a) Young's modulus (Y)
b) Y / (L/A)
c) Y × (A/L)
d) 1 / Y

10. Which of the following is a necessary precaution while performing this experiment?
a) Apply the load suddenly
b) Measure the diameter only at one point
c) Ensure the load does not exceed the elastic limit
d) Use a very short wire

Answer Key for MCQs:

1. b) Longitudinal Stress to Longitudinal Strain
2. b) N/m²
3. c) Compensate for thermal expansion and yielding of the support
4. d) Screw gauge
5. b) Stress is directly proportional to Strain
6. c) Remain unchanged (Young's modulus depends on the material, not dimensions)
7. d) Extension produced by mass M
8. d) Long and thin (Longer L and smaller r² increase 'l' for a given M)
9. c) Y × (A/L) [Since Y = (Mg/l) * (L/A), therefore Mg/l = Y * (A/L)]
10. c) Ensure the load does not exceed the elastic limit

Study these notes thoroughly. Understanding the theory, the apparatus, the formula, and especially the precautions and sources of error is key to mastering this topic for your exams. Good luck!