Physics Class 10 Practical Based Assessment PBA | Federal Board | FBISE | Notes | Worksheets | Concept Based Question

Class: Grade 10 Physics (SSC-II)
Board: Federal Board | FBISE | National Curriculum Pakistan
Topic: Practical Based Assessment (PBA)
Purpose: To help students understand experimental concepts, formulas, procedures, and viva questions for physics practical exams.
Difficulty Level: Conceptual + Exam Preparation Part: 1 Major Experiments

Vernier Calliper Practicles

Objective: To measure the radius and length of a solid metallic cylinder using Vernier callipers and report values with the correct number of significant figures.

Core Objective

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Apparatus

• Vernier Callipers
• Solid metallic cylinder
• Magnifying glass

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Key Definitions & Formulas

• Least Count (LC): The smallest measurement an instrument can take.

  $$LC = \frac{\text{Value of one main scale division}}{\text{Total number of vernier divisions}}$$

  • Example: $1\text{ mm} / 10 = 0.1\text{ mm} = 0.01\text{ cm}$.
• Total Reading: Calculated as $MSR + (VSD \times LC)$.
• Zero Error (ZE): Occurs when the zeros of the main scale and vernier scale do not coincide when jaws are closed.
• Zero Correction (ZC): The negative of Zero Error; applied to the observed reading to get the true value.
• Radius ($r$): Half of the mean diameter ($D/2$).
• Area of Cross-section ($A$): Calculated using the formula $A = \pi r^2$.

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Measurement Procedure

1. Check for Zero Error: Close the jaws and note any misalignment to apply correction later.
2. Measure Diameter:
   • Place the cylinder between the outer jaws.
   • Record the Main Scale Reading (MSR) and the Vernier Scale Division (VSD) that coincides with the main scale.
   • Repeat three times in different orientations to account for irregularities.
3. Measure Length: Place the cylinder lengthwise between the jaws and record three readings to compute the mean.
4. Calculate Means: Find the average diameter and average length to reduce random errors and increase accuracy.

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Critical Thinking & Practical Tips

• Precision: Vernier callipers are preferred over simple rulers because they have a smaller least count ($0.01\text{ cm}$ vs $0.1\text{ cm}$), allowing for more precise results.
• Handling: Jaws must be closed gently. Pressing too tightly can deform the object or damage the instrument, leading to systematic errors.
• Parallax Error: To ensure accuracy, the observer’s eye must be directly in line with the scale reading.
• Environmental Factors: Temperature changes can cause metallic cylinders to expand or contract, affecting the measurement.
• Data Recording: Recording MSR and VSD separately is vital for verifying calculations and ensuring the least count is applied correctly.

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Summary of Error Impact

• Positive Zero Error: Results in readings larger than the actual value; must be subtracted.
• Larger Least Count: Results in lower precision and fewer significant figures in the final report.

Measuring Thickness and Precision

Objective: To measure the diameter (thickness) of a metallic wire using Vernier calipers and determine the measurement's precision.

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Practical 2A: Thickness of a Metallic Wire (Vernier Calipers)

Key Definitions & Formulas:

• Least Count (LC): The smallest measurement an instrument can take.
  $$LC = \frac{\text{Value of 1 main scale division (MSD)}}{\text{Total number of vernier divisions (VSD)}}$$
  • Example from text: $0.1 \text{ mm}$ or $0.01 \text{ cm}$.
• Observed Diameter ($Y$): $Y = M + X$, where $M$ is the Main Scale Reading and $X$ is the fractional part (Vernier scale division $n \times LC$).
• Corrected Diameter ($D$): $D = Y \pm \text{Zero Correction (ZC)}$.

Procedure:

1. Find the Least Count of the instrument.
2. Check for Zero Error by closing the jaws. Calculate Zero Correction (ZC) if the zeros do not align.
3. Place the metallic wire gently between the outer jaws.
4. Record the Main Scale Reading (MSR) just before the vernier zero.
5. Identify the Vernier division (n) that coincides perfectly with any main scale division.
6. Multiply $n$ by $LC$ to get the fractional part ($X$).
7. Add the MSR ($M$) and $X$ to get the observed diameter ($Y$).
8. Repeat at three different positions to calculate the mean diameter.

Critical Insights:

• Precision: Measurement precision is limited by the instrument's Least Count ($0.1 \text{ mm}$).
• Parallax Error: Avoided by viewing the scale readings straight-on.
• Averaging: Multiple readings account for non-uniformity or "ovality" in the wire, providing a reliable mean value.

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Practical 2B: Thickness of a Metallic Wire (Screw Gauge)

Objective: To measure the thickness of a metal strip or wire and calculate its area of cross-section using a screw gauge.

Key Components & Formulas:

• Least Count (LC):
  $$LC = \frac{\text{Pitch of the screw}}{\text{Total divisions on the circular scale}}$$
  • Example from text: $0.01 \text{ mm}$.
• Area of Cross-section ($A$): Derived from the radius ($r$) of the wire.
  $$A = \pi r^2$$

Procedure:

1. Determine the Least Count of the screw gauge.
2. Check for Zero Error by rotating the ratchet until the spindle and anvil touch.
3. Place the wire between the anvil and spindle; tighten the ratchet until it clicks.
4. Note the Main Scale Reading (MSR) visible on the sleeve.
5. Note the Circular Scale Division (n) coinciding with the datum line.
6. Calculate the fractional part ($n \times LC$) and add it to the MSR to get the observed thickness.
7. Apply Zero Correction to find the corrected diameter ($D$).
8. Calculate the mean diameter, radius ($r = D/2$), and final area of cross-section.

Important Precautions:

• Ratchet Use: Always use the ratchet, not the thimble, to avoid flattening the wire with undue pressure.
• Back-lash Error: To minimize this, always move the screw in the same direction when taking measurements.
• Perpendicular Readings: Measure the diameter in two perpendicular directions at each point to ensure accuracy.

Acceleration of a Ball on an Inclined Plane

Objective: To study the motion of a ball rolling down an angle iron by measuring time intervals across different distances and determining acceleration through a distance-time graph.

Apparatus and Materials

• Angle Iron: A 2-meter long track with a fixed stopper at the lower end.
• Support: An iron stand with a V-shaped groove to hold the iron in position.
• Measuring Tools: Meter-rod and set square.
• Timing & Graphing: Steel ball, stopwatch, and graph paper.

Experimental Procedure

1. Preparation: Clean the inner surface of the angle iron and the ball to reduce friction.
2. Setup: Set the apparatus with a small angle of inclination, specifically not more than $15^\circ$.
3. Positioning: Place the ball at a high starting point (e.g., 200 cm or 250 cm). Use a set square to ensure the front of the ball aligns perfectly with the position mark.
4. Timing: Release the ball gently without a push to ensure the initial velocity ($V_i$) is zero. Start the stopwatch on release and stop it when the ball hits the stopper.
5. Data Collection: Repeat the timing for each distance at least twice ($t_1, t_2$) to find the average time ($t$).
6. Variation: Repeat the experiment for at least six different release positions at regular intervals.
7. Calculation: Determine the values for $2S$ (double distance) and $t^2$ (time squared) for each observation.

Mathematical Basis

• Equation used: $S = V_i t + \frac{1}{2}at^2$.
• Simplified Formula: Since the ball starts from rest ($V_i = 0$), the equation becomes $2S = at^2$.
• Acceleration Calculation: Acceleration ($a$) can be calculated as $a = \frac{2S}{t^2}$.
• Units: In this experiment, acceleration is measured in $cm \cdot s^{-2}$ or $m \cdot s^{-2}$.

Graphical Analysis

• Plotting: Plot $2S$ on the horizontal ($x$-axis) as the independent variable and $t^2$ on the vertical ($y$-axis) as the dependent variable.
• Linear Relationship: The relationship between $2S$ and $t^2$ is linear, which allows acceleration to be determined directly from the slope.
• Slope to Acceleration: The slope ($m$) of the graph represents $\frac{1}{a}$. Therefore, $Acceleration (a) = \frac{1}{slope}$.

Critical Concepts and Troubleshooting

• Angle of Inclination: Keeping the angle below $15^\circ$ ensures motion is controlled and uniform while minimizing air resistance and surface effects.
• Initial Velocity: The ball must be released gently because a push would add initial velocity, violating the assumption that $V_i = 0$.
• Error Reduction: Taking multiple time readings ($t_1, t_2, t_3$) for each distance minimizes random human reaction time errors.
• Real-world Factors: Calculated acceleration may be lower than theoretical values due to rolling friction, air resistance, and surface irregularities.
• Improving Accuracy: Accuracy can be improved by using electronic timers or light gates, increasing the number of trials, and lubricating the angle iron to reduce friction.

The Simple Pendulum

Objective: To determine the time period of a simple pendulum and investigate the relationship between its length and time period.

1. Core Concepts and Formulas

• Time Period ($T$): The time taken for one complete vibration.
• Effective Length ($l$): The distance from the point of suspension to the center of the bob. Calculated as: $l = l_1 + r$ (where $l_1$ is thread length and $r$ is the radius of the bob).
• Acceleration due to Gravity ($g$): Calculated using the formula:$$g = 4\pi^2 \left(\frac{l}{T^2}\right)$$
• Proportionality:
  • $T^2 \propto l$ (Time period squared is directly proportional to length).
  • $T \propto \sqrt{l}$ (Time period is directly proportional to the square root of length).

2. Experimental Procedure

1. Measure the diameter of the bob using vernier calipers to find its radius ($r$).
2. Tie a thread (approx. 1 meter) to the bob and pass it through a split cork held by a clamp.
3. Adjust the length of the pendulum ($l$) and ensure the bob is a few centimeters above the floor.
4. Mark the mean position on the floor and two extreme positions (approx. 4–5 cm from the center).
5. Displace the bob to an extreme position and release it.
6. Use a stopwatch to record the time for 20 vibrations.
7. Divide the total time by 20 to find the time period ($T$).
8. Repeat the process with different lengths to observe changes in $T$.

3. Velocity and Energy in SHM

• Maximum Velocity: Occurs at the mean position (equilibrium).
• Minimum Velocity: Occurs at the extreme positions (zero velocity).
• Energy Transformation:
  • At mean position, Kinetic Energy (K.E.) is maximum and Potential Energy (P.E.) is minimum.
  • At extreme positions, P.E. is maximum and K.E. is minimum.

4. Critical Thinking & Viva Questions

• Why measure to the center of the bob? The mass of the bob is concentrated at its center; measuring only to the top would result in an incorrect (shorter) length.
• Why use 20 vibrations instead of one? To reduce human reaction time errors and obtain a more accurate average time.
• Why keep amplitude small? For Simple Harmonic Motion (SHM), the restoring force must be proportional to displacement. Large amplitudes deviate from this rule.
• Why use a heavy bob? A metallic bob has higher density, minimizing the impact of air resistance compared to a light plastic one.
• Significance of the split cork: It provides a firm, fixed point of suspension and ensures the length remains constant during oscillation.
• Sources of Error:
  • Air resistance slowing the bob.
  • Human reaction time when starting/stopping the stopwatch.
  • Friction at the point of suspension.

5. Accuracy Tips

• Ensure the pendulum swings in a single vertical plane without spinning.
• Use a fine, inextensible thread to prevent stretching.
• Perform the experiment in a draft-free environment to minimize air interference.

Specific Heat Capacity

Objective: To determine the specific heat capacity of a liquid (water) or a metal (lead shots) by applying the method of mixtures.

Core Concepts & Definitions

• Heat: The total kinetic energy of the molecules within a body.
• Specific Heat: The amount of thermal energy required to increase the temperature of 1 kg of a substance by 1 K (or 1°C).
• Law of Heat Exchange: Based on Prevost’s theory, in an isolated system, Heat Lost = Heat Gained.
• Polystyrene Cup: Chosen as a calorimeter because it is a non-conductor. Its specific heat is considered negligible (zero) for the purpose of this experiment as it does not radiate heat.

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Apparatus & Materials

• Heating Source: Hypsometer, spirit lamp, or gas burner.
• Measurement Tools: Physical balance, weight box, and two thermometers.
• Containment: Polystyrene cup with lid and stirrer, metallic test tube.
• Samples: Lead shots and water.

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Experimental Procedure

1. Prepare the Solid: Place lead shots into the metallic test tube of the hypsometer.
2. Heating: Fix the test tube so it is above the water surface. Heat until the water boils and the lead shots reach a steady high temperature ($t_2$).
3. Mass Measurement:
   • Weigh the empty polystyrene cup ($m_1$).
   • Fill the cup halfway with water and weigh it again ($m_2$).
4. Initial Temperature: Record the temperature of the cold water in the cup ($t_1$).
5. Mixing: Quickly transfer the hot lead shots from the hypsometer into the polystyrene cup.
6. Final Equilibrium: Stir the mixture gently until the temperature becomes uniform. Record this final temperature ($t_3$).
7. Final Mass: Weigh the cup containing water and lead shots ($m_3$) to determine the mass of the lead.

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Calculations & Formulas

The experiment relies on the equilibrium equation:

Heat lost by lead shots = Heat gained by water

$$M_2 C_2 T_2 = M_1 C_1 T_1$$

• $M_1$ (Mass of water): $m_2 - m_1$
• $M_2$ (Mass of lead): $m_3 - m_2$
• $T_1$ (Rise in water temp): $t_3 - t_1$
• $T_2$ (Fall in lead temp): $t_2 - t_3$
• $C_1$: Specific heat of water ($4200 \text{ J kg}^{-1} \text{K}^{-1}$).
• $C_2$: Specific heat of lead (The value to be calculated).

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Critical Thinking & Accuracy

• Minimizing Error: Transfer lead shots quickly to avoid heat loss to the air, which would lead to an underestimation of specific heat.
• Stirring Technique: Stir gently to ensure uniform heat distribution without losing heat to the surroundings through vigorous movement.
• Safety & Precision: Ensure the test tube does not touch the boiling water directly; it should be heated by steam to maintain a constant, uniform temperature.
• Conservation of Energy: The experiment demonstrates that the total heat lost by the hot substance equals the total heat gained by the cold substance, illustrating energy conservation.

Temperature-Time Graph & Phase Changes

Objective: To study the heating curve of ice and water, specifically identifying the points of Latent Heat of Fusion and Latent Heat of Vaporization using the method of mixtures.

• Apparatus: Beaker, thermometer, stopwatch, Bunsen burner, stirrer, and wire gauze.
• Key Requirement: Use pure ice and clean water. Impurities distort the graph by melting ice below 0°C and raising the boiling point of water above 100°C.

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2. The Heating Process (Step-by-Step)

1. Initial State: Ice is heated from sub-zero temperatures (e.g., -20°C). The temperature rises until it reaches 0°C.
2. Phase Change 1 (Melting): At 0°C, the temperature remains constant. All heat energy is absorbed as Latent Heat of Fusion to overcome molecular bonds and change state from solid to liquid.
3. Liquid Heating: Once all ice is melted, the temperature rises steadily from 0°C to 100°C. The added heat increases the kinetic energy of the water molecules.
4. Phase Change 2 (Boiling): At 100°C, the temperature plateaus again. This is the Latent Heat of Vaporization, where energy is used to convert water into steam.

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3. Graph Interpretations

• Slope of the Line: Represents the rate of heating. A steeper slope indicates faster heating.
• Horizontal Segments: Represent the duration of a phase change. The length of the 100°C segment is longer than the 0°C segment because vaporization requires significantly more energy than melting.
• Identifiable Quantities:
  • Heat Energy (Q): Calculated as $Q = P \times t$ (Power of burner × time).
  • Latent Heat (L): Determined via $L = \frac{Q}{m}$.

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4. Critical Factors for Success

• Atmospheric Pressure: If performed at high altitude, the boiling point decreases (appears lower than 100°C on the graph) because of lower atmospheric pressure.
• Flame Intensity: If the flame intensity is doubled, the slope becomes steeper and the horizontal segments become shorter, though the actual melting/boiling temperatures remain unchanged.
• Measurement Accuracy: To avoid parallax error, keep the thermometer bulb fully immersed and read the scale at eye level when the pointer is stable.

Series Combination of Resistors

Objective: This study guide covers the experimental study of combining resistors in a series circuit to determine the effect on total (equivalent) resistance.

Core Concept

• In a series combination, resistors are connected end-to-end (the right end of one resistor is connected to the left end of the next).
• There is only one path for the current to flow.

Apparatus Required

• Standard resistors ($8.2 \Omega$, $10 \Omega$, and $12 \Omega$).
• Variable power supply (0–12V, 3A).
• Voltmeter (0–10V) and Ammeter (0.6A–3A).
• Rheostat, connecting wires, and a key.

Key Characteristics

1. Current ($I$): The same amount of current flows through each resistor ($I = I_1 = I_2 = I_3$).
2. Voltage ($V$): The total potential difference across the combination is the sum of individual voltage drops ($V = V_1 + V_2 + V_3$).
3. Equivalent Resistance ($R_e$): The total resistance is the sum of all individual resistances ($R_e = R_1 + R_2 + R_3$).
4. Magnitude: The equivalent resistance is always greater than any individual resistance in the circuit.

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Derivation of Formula

Using Ohm’s Law ($V = IR$):

• Individual voltage drops: $V_1 = IR_1, V_2 = IR_2, V_3 = IR_3$.
• Total voltage: $V = V_1 + V_2 + V_3$.
• Substituting Ohm's Law: $IR_e = I(R_1 + R_2 + R_3)$.
• Final Formula: $R_e = R_1 + R_2 + R_3$.

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Critical Thinking: Questions & Answers

Q: Why does total resistance increase in series?
A: Because the current must pass through each resistor sequentially; the total opposition is the sum of all individual oppositions.

• Broken Circuits: If one resistor is removed or fails, the circuit becomes "open," and the current stops flowing entirely. This is why series circuits are not used for household wiring.
• Voltage Distribution: Potential difference across each resistor is different if their resistances are different. Voltage is directly proportional to the resistance ($V \propto R$).
• Power Consumption: If the supply voltage remains constant, adding more resistors in series increases total resistance, which decreases the total current and total power consumption ($P = V^2 / R$).
• Role of the Rheostat: It is used to vary the current in the circuit to take multiple readings without changing the resistors themselves.

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Parallel Combination of Resistors

Objective: To study the effect of combining resistors in parallel and to determine the total (equivalent) resistance of the circuit.

Key Concepts & Definitions

• Parallel Combination: A circuit where resistors are connected in different branches, providing multiple paths for current flow.
• Voltage ($V$): In a parallel circuit, the potential difference across all resistors is the same ($V = V_1 = V_2 = V_3$).
• Current ($I$): The total current is the sum of the currents flowing through each individual branch ($I = I_1 + I_2 + I_3$).
• Equivalent Resistance ($R_{eq}$): The total resistance of the combination, which is always less than the value of the smallest individual resistor.

Experimental Procedure

1. Assembly: Connect resistors, voltmeter, ammeter, rheostat, and power supply as shown in the circuit diagram.
2. Initial Setup: Keep keys open and set the rheostat to the middle position.
3. Measurement: Close the circuit and adjust the rheostat to maintain a constant voltage ($V$).
4. Data Collection: Record the current ($I$) for each resistor individually and then for the combined circuit.
5. Calculations: Use Ohm’s Law to find individual resistances and the equivalent resistance.

Mathematical Formulas

• Ohm’s Law: $V = IR$ or $I = \frac{V}{R}$
• Total Current: $I = I_1 + I_2 + I_3$
• Equivalent Resistance Calculation: $$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$
• For 'n' Resistors: $$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}$$

Critical Characteristics

• Independent Functioning: Each resistor in a parallel circuit operates independently of the others.
• Resistance Trend: The total resistance decreases as more resistors are added because more paths for current are created.
• Current Distribution: Current is inversely proportional to the resistance of the branch (higher resistance = lower current).

Critical Thinking & Practical Application

• The Role of the Rheostat: Used to adjust and maintain a stable voltage across the resistors during the experiment.
• Why $R_{eq}$ is Small: Adding paths reduces the overall opposition to current, similar to adding lanes to a highway to reduce traffic.
• Real-World Use: Parallel wiring is used in household circuits so each appliance receives the same voltage and can operate independently.

Class: Grade 10 Physics (SSC-II)
Board: Federal Board | FBISE | National Curriculum Pakistan
Topic: Practical Based Assessment (PBA)
Purpose: To help students understand experimental concepts, formulas, procedures, and viva questions for physics practical exams.
Difficulty Level: Conceptual + Exam Preparation Part: 2 Minor Experiments

Spring Constant of a Helical Spring

Objective: To determine the spring constant of a helical spring by plotting and analyzing a load-extension graph.

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Key Theory (Hooke's Law)

• Definition: The extension ($x$) of a spring is directly proportional to the applied load ($F$), provided the elastic limit is not exceeded.
• Formula: $$F \propto x \quad \text{or} \quad F = Kx$$
• Spring Constant ($K$): The proportionality constant, also known as the force constant.

Apparatus & Materials

• Helical spring with pointer and rigid stand.
• Slotted weights and hanger.
• Half-meter rod (vertical scale).

Experimental Procedure

1. Setup: Suspend the spring from the rigid support and attach the hanger.
2. Initial State: Note the pointer position ($P_0$) with no weight added. Ensure the pointer moves freely without touching the scale.
3. Loading: Add a slotted weight. Note the pointer position ($P_1$). Repeat this at least six times with equal weight increments.
4. Unloading: Remove weights one by one, noting the pointer position ($P_2$) at each step.
5. Data Processing: Calculate the mean position ($P$) of loading and unloading for each weight. Determine extension using $x = P - P_0$.

Observations & Graphing

• Plotting: Draw a graph with Load ($F$) on the x-axis and Extension ($x$) on the y-axis.
• Result: A straight line through the origin confirms $F \propto x$.
• Slope Significance: The slope represents the spring constant ($K$).
  • A steeper slope indicates a stiffer/thicker spring.
  • A gentler slope indicates a more flexible spring.

Critical Thinking & Precautions

• Elastic Limit: Do not overload the spring. Exceeding the limit causes permanent deformation, and the graph will no longer be linear.
• Parallax Error: Keep your eye level with the pointer when taking readings to ensure accuracy.
• Stability: Switch off fans to minimize air currents that cause the spring to oscillate.
• Error Reduction: Taking both loading and unloading readings helps detect hysteresis and ensures the spring recovers elastically.

Finding the Centre of Gravity (C.G.)

Objective:To determine the exact position of the Centre of Gravity (C.G.) of an irregular, thin plane lamina using the plumb line method.

Essential Materials

• A thin lamina: Irregularly shaped.
• Plumb line: A string with a weight used to find a vertical line.
• Support: Retort stand, drawing board, or wall support with pins.
• Tools: Pencil, marker, and a scale/ruler for tracing.

Step-by-Step Procedure

1. Suspend the Lamina: Fix a pin through any point on the edge of the lamina so it hangs freely.
2. Align Plumb Line: Hang the plumb line from the same pin and wait for it to come to a complete rest.
3. Trace the Line: Use a pencil and ruler to mark the straight vertical line of the plumb line across the lamina.
4. Repeat for Accuracy: Repeat this process from at least two other different points on the lamina's edge.
5. Find the Intersection: The point where all three traced lines meet is the Centre of Gravity (C.G.).

Critical Observations

• Variables: Points ($P_1, P_2, P_3$) and Traced Lines ($L_1, L_2, L_3$).
• Method: This is a graphical intersection method; no complex numerical calculations are required.
• Result: The C.G. always lies at the intersection of the plumb line traces.

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Critical Thinking Questions & Answers

• Earth’s Gravity: A plumb line always points toward the center of the Earth because it aligns with gravitational force, making it a perfect vertical reference.
• Equilibrium: The C.G. lies vertically below the suspension point for any orientation; intersecting lines meet at the true C.G.
• Why Three Points? Suspending from at least three points increases accuracy and ensures that small errors in drawing one or two lines don't affect the final intersection point.
• Non-Uniform Shapes: If a lamina is non-uniform (heavier on one side), the C.G. shifts toward the heavier side and no longer lies at the geometric centre.
• Uniform Triangular Shapes: For a triangular uniform lamina, the C.G. lies at the centroid (the intersection of the medians).
• Suspension at C.G.: If suspended exactly through its C.G., the lamina remains perfectly balanced in any orientation because the line of action of its weight passes through the suspension point.
• Calculation vs. Experiment: Experimental methods are easier for irregular shapes because their mass distribution is uneven and difficult to express mathematically.

Density of an Irregular Stone

Objective:To determine the volume of an irregular, insoluble stone using the water displacement method and subsequently calculate its density.

Essential Formulas

• Volume of Stone ($V$): $V = V_2 - V_1$
• Density ($\rho$): $\rho = \frac{m}{V}$
• Variables: $m$ = mass, $V$ = volume, $V_1$ = initial water level, $V_2$ = final water level.

Step-by-Step Procedure

1. Measure Mass: Use a balance to find the mass ($m$) of the stone and record it in grams (g).
2. Initial Volume: Fill a measuring cylinder partly with water and note the initial level ($V_1$) in $cm^3$ or $ml$.
3. Submerge: Tie the stone with a thin thread and lower it gently into the cylinder to avoid air bubbles or splashing.
4. Final Volume: Note the new water level ($V_2$) after the stone is fully submerged.
5. Calculation: Subtract $V_1$ from $V_2$ to find the volume, then divide mass by volume to find the density.

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Critical Thinking & Conceptual Insights

Methodology & Accuracy

• Why Displacement? Irregular objects do not have regular dimensions (like cubes or spheres), so standard geometric formulas cannot be used. Displacement directly measures the space the object occupies.
• Controlled Entry: The stone must be lowered slowly to avoid splashing or loss of water, which would distort the final volume measurement.
• Air Bubbles: If bubbles stick to the stone, they increase the apparent volume of displaced water, making the calculated density inaccurate.

Material Constraints

• Insolubility: The stone must be insoluble. If it dissolves, the mass and water level would change, leading to incorrect results.
• Apparatus Choice: A measuring cylinder is better than a beaker because its narrow cross-section and clear markings allow for precise measurement of small volume changes.

Scientific Principles

• Archimedes’ Principle: The experiment relies on the fact that the volume of water displaced is exactly equal to the volume of the submerged object.
• Porous Materials: If a stone has tiny pores, water enters them, causing the displaced volume to be less than the actual volume. This leads to an overestimated density.
• Characteristic Property: Density is a characteristic property because it remains constant for a pure substance regardless of size or shape, making it vital for material identification.

Laws of Reflection using a Plane Mirror

Objective:To verify the two fundamental laws of light reflection using a plane mirror.

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Core Concepts & Aim

• The Laws to Verify:
  1. The angle of incidence ($i$) is equal to the angle of reflection ($r$).
  2. The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane.

Materials Required

• Plane mirror and drawing board with a white sheet.
• Protractor, scale (ruler), and a sharp pencil.
• Optical pins (4–6).

Experimental Procedure

1. Preparation: Fix the paper on the board and draw line MN to represent the mirror position.
2. The Normal: Draw a line ON perpendicular to MN at point O (the point where light will strike).
3. Setting the Angle: Draw an incident ray IO at a specific angle ($i$). Place two pins, P and Q, vertically on this line.
4. Mirror Alignment: Place the mirror vertically along line MN.
5. Locating the Reflection: Look into the mirror from the other side of the normal. Place pins R and S so they appear in a straight line with the images of pins P and Q.
6. Finalizing: Remove the mirror. Join R and S to meet at point O. This line (OS) is the reflected ray.
7. Measurement: Use a protractor to measure angles $i$ and $r$. Repeat for multiple angles (e.g., 20°, 30°, 40°).

Observations and Calculations

Observation No.	Angle of Incidence (i)	Angle of Reflection (r)
1	20°	20°
2	30°	30°
3	40°	40°

Critical Thinking: Troubleshooting & Accuracy

• Why use a Normal? Measuring angles relative to the normal ensures consistency and is the standard way reflection laws are defined.
• Mirror Placement: If the mirror is not exactly on line MN or is tilted, the rays will not align properly, leading to incorrect angle measurements.
• Avoiding Parallax Error: Always view the base of the pins. Viewing from the tops introduces alignment errors that affect the accuracy of the reflected ray.
• Significance of Multiple Trials: Repeating the experiment with different angles confirms that $i = r$ is a universal law, not a localized coincidence.
• Surface Texture: If the mirror were rough, light would scatter (diffused reflection), making it impossible to measure a distinct reflected ray or verify the laws.

Conclusion

• The experiment confirms that $i = r$ within experimental error.
• Since all lines are drawn on a single flat sheet of paper, it proves the incident ray, reflected ray, and normal are coplanar.

Refraction Through a Glass Slab

Objective:This study guide covers the essential concepts and procedures for the Class 10 Physics Practical Based Assessment (PBA) regarding light refraction in a rectangular glass slab.

Core Concepts & Definitions

• Refraction: The process where light bends as it passes from one medium (air) into another of different optical density (glass).
• Snell’s Law: A law stating that the ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) is a constant, known as the refractive index ($n$).
  Formula: $$n = \frac{\sin i}{\sin r}$$
• Lateral Displacement: The perpendicular distance between the path of the original incident ray and the emergent ray.

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Experimental Procedure

1. Setup: Fix a white sheet on a drawing board and trace the boundary of the glass slab (labeled $ABCD$).
2. Incident Ray: Draw an oblique line ($MY$) to represent the incident ray and place two pins ($P$ and $Q$) vertically on this line.
3. Observation: Look through the opposite side of the glass slab. Place two more pins ($R$ and $S$) so they appear to be in a perfectly straight line with the images of $P$ and $Q$.
4. Tracing the Path: Remove the slab and pins. Draw a line through $R$ and $S$ to meet the boundary at point $Y'$. Join $Y$ and $Y'$ to show the path of light inside the glass.
5. Measurement: Draw normals at points $Y$ and $Y'$. Use a protractor to measure the angle of incidence ($i$) and the angle of refraction ($r$).

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Key Observations & Conclusions

• Bending Direction: When light travels from a rarer medium (air) to a denser medium (glass), the ray bends toward the normal.
• Angle Equality: In a rectangular slab, the angle of incidence ($i$) and the angle of emergence ($e$) are equal.
• Constant Ratio: For different angles of incidence, the ratio $\frac{\sin i}{\sin r}$ remains constant, providing a mean refractive index of approximately 1.52 for glass.

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Critical Thinking Questions & Answers

Q: Why is the angle of refraction always less than the angle of incidence here?

Because glass is optically denser than air. Light slows down upon entering, causing the ray to bend toward the normal.

Q: Why must the incident ray be drawn obliquely (at an angle)?

At a perpendicular incidence (90° to the surface), light does not bend ($i = 0, r = 0$). This makes it impossible to verify Snell's law or observe refraction.

Q: What is the significance of using sines ($\sin i / \sin r$) instead of just the angles ($i / r$)?

Snell’s Law is specifically based on the ratio of the trigonometric sines of the angles to accurately determine the constant refractive index of a material.

Q: What would happen if the glass slab did not have parallel surfaces?

The emergent ray would not be parallel to the incident ray, and the angle of emergence would not equal the angle of incidence.

Q: How does lateral displacement occur?

As light bends twice (once entering and once leaving), it follows a shifted path. While the emergent ray is parallel to the incident ray, it is displaced sideways.

Finding the Critical Angle of a Prism

Objective:This study guide covers the essential concepts and procedures for Finding the Critical Angle of a Prism

• Refraction: The bending of light as it passes from a denser medium (glass) to a rarer medium (air).
• Critical Angle ($C$): The specific angle of incidence in the denser medium for which the angle of refraction is 90°.
• Total Internal Reflection (TIR): This occurs when the angle of incidence exceeds the critical angle ($\theta_i > C$), causing the light to reflect entirely back into the denser medium.
• Refractive Index Formula: The relationship is defined as:

  $$n = \frac{1}{\sin C}$$

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Experimental Procedure

1. Initial Trace: Place the glass prism on a drawing board and trace its boundary ($ABC$) with a sharp pencil.
2. Object Pin: Fix a pin ($P$) against the face $AB$ so it touches the glass.
3. Observation: Look through the opposite face ($AC$) to find the image of pin $P$.
4. Finding the Limit: Slowly move your eye from $C$ toward $A$ until the image of $P$ becomes very faint and just begins to disappear.
5. Alignment: Fix two pins ($Q$ and $R$) at least 5 cm apart so they are in a straight line with the faint image of $P$.
6. Geometric Construction:
   • Draw a perpendicular $PL$ from $P$ to the base $BC$. Extend it to $D$ so $PL = LD$.
   • Join $D$ to $S$ (the point where the line from $Q$ and $R$ meets face $AC$).
   • The intersection of $DS$ and $BC$ is marked as $M$.
7. Measurement: Measure the angle $\angle PMS$. The critical angle $C$ is calculated as:

   $$C = \frac{1}{2} \angle PMS$$

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Critical Thinking Questions & Answers

• Why is the image faint at the critical angle? Because the refracted ray travels along the prism surface, very little light enters the air to reach the eye.
• Why must pins $Q$ and $R$ be 5 cm apart? A larger distance reduces angular error and increases the accuracy of the traced ray.
• What happens if the angle of incidence is greater than $C$? The ray will not emerge; it undergoes Total Internal Reflection and bounces back into the prism.
• Why is the base of the prism kept away from the observer? This orientation ensures the critical angle can be measured accurately and aligns the viewing direction with the refracted path.

Measuring Current and Voltage (V-I Characteristics)

Objective: To measure the current ($I$) and voltage ($V$) across a resistor (Nichrome wire) and plot the $V-I$ characteristics to understand their relationship.

Materials Required

• Conductor: Nichrome wire (resistance not less than $10\ \Omega$).
• Measuring Instruments: Voltmeter ($0-15\text{V}$) and Ammeter ($0-0.6\text{A}$).
• Control & Power: Rheostat ($50\ \Omega$), Power supply ($0-12\text{V}, 1\text{A}$), and a Key.
• Basics: Connecting wires and sandpaper.

Procedure

1. Setup: Draw and connect the circuit as shown in the diagram, ensuring the Ammeter is in series and the Voltmeter is in parallel with the Nichrome wire.
2. Initial Adjustment: Before starting, move the rheostat slider to the middle position to avoid sudden high currents.
3. Power On: Turn the power supply ON and close the key.
4. Data Collection: Slowly rotate the rheostat knob. Record the Voltmeter ($V$) and Ammeter ($I$) readings.
5. Calculations: Determine the resistance ($R$) for each reading using the formula: $$R = \frac{V}{I}$$
6. Repeat: Take at least four more readings by changing the resistance of the rheostat.

Observations & Graphing

• Mean Resistance: Calculated by averaging all resistance values (e.g., $\frac{25+25+25+25+25}{5} = 25\ \Omega$).
• V-I Graph: Plotting Voltage ($V$) on the x-axis and Current ($I$) on the y-axis results in a straight line passing through the origin.
• Conclusion: The straight line proves that current ($I$) is directly proportional to the potential difference ($V$), confirming that the resistance ($R$) is constant.

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Critical Thinking: Key Concepts

• Why Nichrome? It has a high, stable resistance and its resistance does not change significantly with small temperature variations, making it ideal for linear $V-I$ measurements.
• Ohm's Law Verification: If the graph is a straight line through the origin, it confirms Ohm's Law ($V = IR$).
• Graph Slope: The slope of the line represents the resistance ($R$). A steeper slope indicates a higher resistance.
• Instrument Placement:
  • Voltmeter: Connected in parallel to measure potential difference across the component.
  • Ammeter: Connected in series to measure the flow of current through the circuit.
• Safety & Errors: If the graph is not straight, it could be due to overheating (which changes resistance), loose connections, or uncalibrated meters.

Potential Difference vs. Wire Length

Objective: To determine how the potential difference ($V$) across a wire varies with its length ($L$) for a steady current, and verify that $V \propto L$.

Core Components & Setup

• Materials Required: Uniform resistance wire (on a metre rule), DC power supply, rheostat (variable resistor), ammeter, voltmeter, connecting wires, crocodile clips, and an optional micrometer for thickness.
• Circuit Arrangement:
  1. The power supply, rheostat, ammeter, and test wire are connected in series.
  2. The voltmeter is connected in parallel across the specific segment of the wire being measured.

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Experimental Procedure

1. Set up the circuit as described, ensuring the voltmeter is connected across length $L$.
2. Use the rheostat to keep the current ($I$) constant throughout the experiment.
3. Measure the potential difference ($V$) for various lengths ($L$) (e.g., 0.10m, 0.20m, 0.30m, etc.).
4. Record the data and plot a graph of $V$ (vertical axis) against $L$ (horizontal axis).

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Key Observations & Results

• The Relationship: The data indicates that as length increases, potential difference increases linearly. The ratio $V/L$ remains constant for a fixed current.
• Conclusion: Potential difference across a uniform wire is directly proportional to its length ($V \propto L$).
• The Linear Graph: A straight-line graph through the origin confirms the relation $V = kL$, where $k$ is the potential gradient.

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Critical Thinking & Concept Summary

• Linear Increase: $V$ increases with $L$ because the resistance of a uniform wire is proportional to its length ($R \propto L$). Since $V = IR$, as $R$ grows with length, so does $V$.
• Importance of Constant Current: If current changes, $V$ would vary with both $I$ and $L$. Keeping $I$ constant isolates the effect of length on voltage.
• Non-Uniform Wires: If the wire thickness or resistivity is not uniform, it causes irregular voltage drops, leading to a non-linear graph and inaccurate potential gradient calculations.
• Calculating Resistivity: Using the potential gradient ($V/L$) and known current, resistance per unit length can be found. Resistivity ($\rho$) can then be computed if the cross-sectional area ($A$) is known: $$R = \rho \frac{L}{A}$$
• Connection Integrity: Clean, tight connections with crocodile clips are essential. Poor contact introduces "extra resistance," causing systematic errors in measurements.