THE PRACTICE STUDIO
Go slowly. Ask why. Make it yours.
PRACTICE / Vernier calipers
Correct a vernier reading
A vernier has least count 0.10 mm. Its main scale reads 12 mm and the sixth vernier division coincides. Its positive zero error is 0.20 mm.
Find the corrected length.
Organize the givens & assumptions
- MS = 12 mm
- n = 6
- LC = 0.10 mm
- zero error = +0.20 mm
Uniform scale divisions, an additive zero offset and jaws seated squarely on the object.
Study with a tutor prompt
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Problem: Correct a vernier reading
A vernier has least count 0.10 mm. Its main scale reads 12 mm and the sixth vernier division coincides. Its positive zero error is 0.20 mm.
Question: Find the corrected length.
Givens:
- MS = 12 mm
- n = 6
- LC = 0.10 mm
- zero error = +0.20 mm
Assumptions: Uniform scale divisions, an additive zero offset and jaws seated squarely on the object.
Choices (LaTeX):
A. 11.8\ \mathrm{mm}
B. 12.4\ \mathrm{mm}
C. 12.6\ \mathrm{mm}
D. 12.8\ \mathrm{mm}
Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.
Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.Start with the smallest hint.
Work through it with me.
One decision at a time. Pause, predict, then unpack the algebra.
Add the fine-scale contribution, then subtract the known positive offset.
Choose a physical relation
The coincident vernier division supplies the fraction beyond the main-scale mark; zero error is an offset in the indicated reading.
Isolate what is asked
Add the fine-scale contribution, then subtract the known positive offset.
Why is this step valid?
A positive zero error means the instrument reads too high, so subtract 0.20 mm after adding the six vernier increments.
Substitute and interpret
The indicated 12.6 mm becomes 12.4 mm; correcting a positive offset must reduce the reading.
Adding the offset back reproduces the raw observed reading.
TRY THE IDEA AGAIN
If the coincident division changes from six to seven with everything else fixed, how much does the corrected length change?
YOUR LEARNING NOTE
How does this idea feel now?
Confidence is a reflection, not proof of mastery.
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