Vernier Least Count and Direct Reading
For a direct vernier, the least count is one main-scale division minus one vernier-scale division, and the observed reading is the main-scale reading plus the coinciding vernier division multiplied by that least count.
Why this shows up in the exam
Tube diameter measurement · Depth and internal-diameter measurement · Travelling-microscope scale reading
Learn the idea
A vernier resolves the small mismatch between a main-scale division and a vernier-scale division. The two scales almost agree, so the coinciding vernier mark reveals the fraction left beyond the main-scale reading; the instrument turns a small accumulated mismatch into a readable length.
🧠 Memory hook: Main scale gives the whole part; coincidence gives the fraction.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- LC = 1 MSD - 1 VSD — direct-vernier least count; use the actual stated scale relation
- observed reading = MSR + n(LC) — reading when the nth vernier mark coincides, before zero correction
How to approach it
- 1Convert the stated VSD-MSD relation first
- 2Record MSR immediately left of vernier zero
- 3Add coincidence contribution, then apply correction
Common slip-ups that cost marks
- •Multiplying one MSD by the number of vernier divisions
- •Using the coinciding mark as a length without multiplying by LC
- •Applying zero correction before determining its sign
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
In a meter bridge, resistance 2 ohm is in the left gap and balance occurs at 40 cm from the left end. Find the right-gap resistance.
More from Experimental Skills
Vernier Zero Error and Correction
Vernier zero error is the signed reading shown when the jaws are in true contact; the zero correction is its negative, so the corrected measurement equals the observed measurement minus the signed zero error.
Screw-Gauge Pitch and Least Count
The pitch is the axial distance moved by the spindle per complete rotation, and the screw-gauge least count is the pitch divided by the number of equal divisions on the circular scale.
Screw-Gauge Reading and Zero Correction
The observed screw-gauge reading is the pitch-scale reading plus the circular-scale reading times the least count, and the corrected value is obtained by subtracting the signed zero error measured with the studs in contact.
Resolution and Propagation of Measurement Uncertainty
For independent small limiting uncertainties, the maximum fractional uncertainty of a product of powers Q = product(x_i raised to n_i) is the sum of |n_i| times Delta x_i/x_i; a directly read scale cannot justify resolution finer than its least count.
Stokes-Law Viscosity by Terminal Speed
For a small sphere moving slowly through an effectively unbounded Newtonian liquid, Stokes drag is 6 pi eta R v; balancing drag with weight minus buoyancy gives terminal speed proportional to R squared and inversely proportional to viscosity.
Travelling Microscope and Apparent Depth
For near-normal viewing through a plane slab, refractive index is real depth divided by apparent depth; the required depths are differences of corrected travelling-microscope readings, each resolved by its vernier least count.