Numericals on Vernier callipers

📘 NUMERICALS (Vernier Calipers)

Q1. A stopwatch has 10 divisions between 0 and 5 s. What is its least count?

Formula: L.C = total range ÷ number of divisions
= 5 ÷ 10 = 0.5 s

Q2. A vernier has 10 divisions equal to 9 divisions of main scale. If 1 MSD = 1 mm, find least count.

Formula: L.C = value of 1 MSD ÷ number of VSD
= 1 ÷ 10 = 0.1 mm

Q3. A microscope has 20 main scale divisions in 1 cm and 50 vernier divisions equal to 49 MSD. Find least count.

1 MSD = 1/20 = 0.05 cm
L.C = 0.05 ÷ 50 = 0.001 cm

Q4. A boy measures thickness of a pencil as 0.4 mm. If zero error is −0.02 cm, find correct thickness.

0.4 mm = 0.04 cm
Correct = 0.04 − (−0.02) = 0.06 cm

Q5. A vernier calipers has 10 VSD = 9 mm. When jaws are closed, 3rd division coincides. Find zero error.

L.C = 1 ÷ 10 = 0.1 mm
Zero error = 3 × 0.1 = 0.3 mm

Q6. Main scale is in mm and 19 MSD = 20 VSD. Find least count.

L.C = 1 ÷ 20 = 0.05 mm

Q7. While measuring a length, zero error is −0.02 cm. What correction should be applied?

Correction = +0.02 cm
Correct reading = Observed + 0.02 cm

Q8. Vernier scale readings are as shown in the figure. Give the actual reading.
(a) Zero error = +0.02 cm
(b) Zero error = −0.03 cm

📌 Insert Figure Here (Vernier Scale Diagram)

Given:
MSR = 1.1 cm
VSR = 5
L.C = 0.01 cm

Formula: Reading = MSR + (VSR × L.C)
= 1.1 + (5 × 0.01)
= 1.1 + 0.05 = 1.15 cm

(a) Zero error = +0.02 cm
Correct reading = 1.15 − 0.02 = 1.13 cm

(b) Zero error = −0.03 cm
Correct reading = 1.15 − (−0.03)
= 1.15 + 0.03 = 1.18 cm

Q9. While measuring the length of a rod with a vernier calipers, the position of scales is shown below. Find the length of the rod.

📌 Insert Figure Here (Fig. 1.14)

Formula: Reading = MSR + (VSR × L.C)

From diagram (approx):
MSR = 3.4 cm
VSR = 6
L.C = 0.01 cm

Reading = 3.4 + (6 × 0.01)
= 3.4 + 0.06 = 3.46 cm