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.
Why this shows up in the exam
Wire diameter measurement · Sheet thickness measurement · Small-sphere diameter measurement
Learn the idea
A screw gauge converts one rotation into a small axial advance and divides that advance on its circular scale. The screw thread acts like a very shallow ramp wrapped around a cylinder: one turn advances by the pitch, while the circular divisions split that advance into much smaller readable steps.
🧠 Memory hook: One turn gives pitch; one division gives pitch divided by divisions.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- pitch = axial advance / number of rotations — calibration from a measured multi-turn displacement
- LC = pitch / N — resolution for N circular-scale divisions per turn
How to approach it
- 1Find one-turn advance
- 2Divide by circular-scale divisions
- 3Keep pitch and LC in the same length unit
Common slip-ups that cost marks
- •Treating total multi-turn travel as the pitch
- •Multiplying pitch by circular divisions
- •Changing pitch or division count without recomputing LC
🌟 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 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.
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 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.