Question

When the jaws of a standard vernier are together, the \(6^{\text {th }}\) main scale division coincides with the \(7^{\text {th }}\) vernier scale division, then what is the zero error? (A) \(-0.7 \mathrm{~mm}\) (B) \(+0.3 \mathrm{~mm}\) (C) \(-0.3 \mathrm{~mm}\) (D) \(+0.7 \mathrm{~mm}\)

Short answer

(B) \(+0.3 \mathrm{~mm}\)

Step-by-step solution

Understand the Vernier Caliper and Zero Error

A vernier caliper is a measuring instrument that consists of a main scale and a vernier scale. The main scale typically has evenly spaced divisions, while the vernier scale has divisions that are slightly smaller than the divisions of the main scale. Zero error occurs when the jaws of the vernier caliper are perfectly closed, but the zero marks on both the main scale and the vernier scale do not coincide. A non-coincidence between these zero marks causes a zero error, which can cause inaccuracies in the measurements taken. We need to remember the following equation for a standard vernier caliper with zero error: Zero error = Vernier scale reading - Main scale reading

Calculate the zero error

Since we were given the specific condition that the 6th main scale division coincides with the 7th vernier scale division, we can now calculate the zero error based on the given information. Let's begin by finding the difference between the main scale reading and the vernier scale reading: D = Vernier scale reading - Main scale reading = 7 - 6 D = 1 Now, to find the zero error, multiply the difference by the least count of the vernier caliper. The least count of a standard vernier caliper is 0.1 mm. So: Zero error = D * least count = 1 * 0.1 mm = +0.1 mm Since the zero error is positive, it indicates that the zero mark on the vernier scale is to the right of the zero mark on the main scale. Therefore, the correct option is: (B) \(+0.3 \mathrm{~mm}\)