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

Vernier Calliper Practicles

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

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.