Question

A length is measured by a vernier caliper which has positive zero error of 0.3mm. While the measurement of length, it is found that 0 on the vernier scale lies between 6.5cm and 7.5cm. The vernier coincide is 4, then the correct value of measurement of length is (Take least count = 0.01cm )

• A. 6.50cm
• B. 6.51cm
• C. 6.52cm
• D. 6.53cm

Answer 1

Answer: (B)

6.51cm

Answer 2

The measurement using a vernier caliper is given by the formula:

Observed Reading = Main Scale Reading (MSR) + (Vernier Coincidence (VC) $\times$ Least Count (LC))

Given:

• Main Scale Reading (MSR): The zero of the vernier scale lies between 6.5 cm and 7.5 cm. The MSR is the reading on the main scale just before the zero mark of the vernier scale. So, MSR = 6.5 cm.
• Vernier Coincidence (VC): The vernier coincide is 4. This means the 4th division of the vernier scale coincides with a main scale division. So, VC = 4.
• Least Count (LC): LC = 0.01 cm.

Calculate the Observed Reading:

Observed Reading = 6.5 cm + (4 $\times$ 0.01 cm)
Observed Reading = 6.5 cm + 0.04 cm
Observed Reading = 6.54 cm

The vernier caliper has a positive zero error. The formula for the correct measurement is:

Correct Reading = Observed Reading - Zero Error

Given:

Positive Zero Error = +0.3 mm

Convert the zero error to centimeters:

1 cm = 10 mm
0. 3 mm = $\frac{0.3}{10}$ cm = 0.03 cm

So, Zero Error = +0.03 cm.

Calculate the Correct Reading:

Correct Reading = 6.54 cm - 0.03 cm
Correct Reading = 6.51 cm