Question

A Vernier having a positive zero error of +5 is used to measure the side of a 2 cm cube. The length as measured by the Vernier will be: (use LC = 0.01 cm)
A. 1.95 cm
B. 2 cm
C. 2.05 cm
D. Cannot say

Answer 1

Hint: Practically there can’t be a measurement where the error becomes totally zero. Every measurement has a certain amount of error which could be human error, instrument error, or any other error. But it is a good practice to minimize this error as much as possible. If we know the instrumental error, we can also measure the corrected length of the object.

Formula used: Corrected length = Observed length + Correction

Complete step-by-step solution:
Note that the given error (+5) is with respect to the device. Hence it measures $-5 \times 0.01 =- 0.05$, where 0.01 is the LC (Least Count) of the instrument of the device. Now, it is sure by the presence of the error that the observed length is less than the actual length. Hence we can say the corrected length of the caliper is 2 cm as it has to measure the side which is 2 cm. Thus using relation: Corrected length = Observed length + Correction, we get
$2 cm\ =\ Observed\ length\ + (-0.05)$
Or $Observed\ length = 2 + 0.05 = 2.05 cm$
Hence option C is correct.

Additional information: Several times we need to be very precise about our measurements. The most commonly used equipment or device for measurement is scale. It can be used to measure the length in the order of a millimeter. It can’t measure the distance of order one-tenth of milli-meter. Hence the minimum it can measure is called its least-count. But what if we need to calculate even more precisely? In that case, we go for even accurate devices such as screw-gauge and Vernier caliper. The least count of different devices is different. The minimum value of the least count of a device, the accurate is its measurement. The least count of Vernier caliper is 0.01 cm (or 0.1 mm) means it is 10 times more accurate than a meter scale.

Note: One must not confuse with the sign of given error. We are given the error to be positive. This means that the device has such an error, which measures the given dimension giving a positive error which suggests that it measures more than the actual value itself. Hence we must subtract something to get the actual reading and that something is called a correction.