Experimental Skills

This chapter covers the experimental techniques and laboratory skills required for JEE Physics.

Overview

graph TD
    A[Experimental Skills] --> B[Measuring Instruments]
    A --> C[Key Experiments]
    A --> D[Data Analysis]
    B --> B1[Vernier Caliper]
    B --> B2[Screw Gauge]
    B --> B3[Meters]
    C --> C1[Mechanics]
    C --> C2[Electricity]
    C --> C3[Optics]

Measuring Instruments

Vernier Caliper

Least Count:

$$LC = 1 \text{ MSD} - 1 \text{ VSD}$$

Typically: LC = 0.1 mm = 0.01 cm

Reading:

$$\text{Reading} = \text{MSR} + (\text{VSD} \times LC)$$

Measures:

• External diameter
• Internal diameter
• Depth

Screw Gauge

Least Count:

$$LC = \frac{\text{Pitch}}{\text{No. of divisions on circular scale}}$$

Typically: LC = 0.01 mm

Zero Error:

• Positive: Reference line below zero
• Negative: Reference line above zero

Correct reading = Observed reading ± Zero error

Other Instruments

Instrument	Measures	Least Count
Metre scale	Length	1 mm
Stopwatch	Time	0.01 s
Thermometer	Temperature	0.1°C
Ammeter	Current	Depends on range
Voltmeter	Voltage	Depends on range

Key Experiments

1. Simple Pendulum

Objective: Find g by plotting T² vs L

$$T = 2\pi\sqrt{\frac{L}{g}}$$ $$g = \frac{4\pi^2 L}{T^2}$$

Graph: T² vs L is straight line through origin with slope $\frac{4\pi^2}{g}$

2. Young’s Modulus (Searle’s Apparatus)

$$Y = \frac{FL}{A\Delta L} = \frac{4FL}{\pi d^2 \Delta L}$$

Procedure:

1. Measure diameter of wire
2. Apply loads and measure extension
3. Plot F vs ΔL

3. Surface Tension (Capillary Rise)

$$S = \frac{\rho g r h}{2\cos\theta}$$

For water-glass: $\cos\theta = 1$

4. Coefficient of Viscosity

Using Stokes’ law:

$$\eta = \frac{2r^2(\rho - \sigma)g}{9v_t}$$

Measure terminal velocity of sphere falling through liquid.

5. Speed of Sound (Resonance Tube)

$$v = 2f(l_2 - l_1)$$

where $l_1$ and $l_2$ are lengths for first and second resonance.

End correction: $e = \frac{l_2 - 3l_1}{2}$

6. Specific Heat Capacity

Using calorimeter:

$$m_1 c_1 (T_1 - T) = m_2 c_2 (T - T_2)$$

7. Resistance (Ohm’s Law)

Plot V vs I graph. Slope = R

$$R = \frac{V}{I}$$

8. Resistivity (Metre Bridge)

$$\frac{R_1}{R_2} = \frac{l}{100-l}$$

Specific resistance: $\rho = \frac{\pi d^2 R}{4L}$

9. Galvanometer

Figure of Merit:

$$K = \frac{E}{(R + G)\theta}$$

Conversion to Ammeter: Shunt $S = \frac{I_g G}{I - I_g}$

Conversion to Voltmeter: High resistance $R_h = \frac{V}{I_g} - G$

10. Focal Length

Convex Lens: Use $u$-$v$ method or displacement method.

$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$

Concave Mirror:

$$f = \frac{uv}{u + v}$$

11. Prism Deviation

$$\delta = i + e - A$$

Minimum deviation: $i = e$

$$n = \frac{\sin\frac{A + D_m}{2}}{\sin\frac{A}{2}}$$

12. Refractive Index (Glass Slab)

Using traveling microscope:

$$n = \frac{\text{Real depth}}{\text{Apparent depth}}$$

Error Analysis

Types of Errors

1. Systematic: Consistent in one direction
2. Random: Irregular, unpredictable
3. Gross: Mistakes

Error Propagation

For $Z = A^a B^b C^c$:

$$\frac{\Delta Z}{Z} = |a|\frac{\Delta A}{A} + |b|\frac{\Delta B}{B} + |c|\frac{\Delta C}{C}$$

Significant Figures

• All non-zero digits significant
• Zeros between digits significant
• Leading zeros not significant
• Trailing zeros after decimal significant

Data Presentation

Graph Rules

1. Choose appropriate scale
2. Plot points clearly
3. Draw best-fit line/curve
4. Label axes with units
5. Give title

Slope Calculation

$$\text{Slope} = \frac{y_2 - y_1}{x_2 - x_1}$$

Choose points far apart on best-fit line.

Practice Problems

1. In a metre bridge experiment, the balance point is at 40 cm. If R = 4 Ω, find the unknown resistance.

2. A vernier has 10 VSD equal to 9 MSD (1 MSD = 1 mm). Find least count.

3. Using resonance tube, first resonance at 17 cm, second at 51 cm. If frequency is 512 Hz, find speed of sound.

Further Reading

• Units and Measurements - Error theory
• Current Electricity - Electrical experiments