Question

A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading : $0\, mm$ Circular scale reading : $52$ divisions Given that $1\, mm$ on main scale corresponds to $100$ divisions on the circular scale. The diameter of the wire from the above data is :

• A. 0.52 cm
• B. 0.026 cm
• C. 0.26 cm
• D. 0.052 cm

Answer 1

The Correct Option is D

To determine the diameter of the wire, we need to understand the readings given by the screw gauge:

The screw gauge uses two scales: the main scale and the circular scale.

The given data is: 

• Main scale reading: \(0\, \text{mm}\)
• Circular scale reading: \(52\) divisions

According to the question, \(1\, \text{mm}\) on the main scale corresponds to \(100\) divisions on the circular scale. Therefore, each division on the circular scale corresponds to:

\(\frac{1}{100}\, \text{mm} = 0.01\, \text{mm}\)

Given the circular scale reading is \(52\) divisions, the value it represents in millimeters is:

\(52 \times 0.01\, \text{mm} = 0.52\, \text{mm}\)

Since the main scale reading is \(0\, \text{mm}\), the total reading (which is the diameter of the wire) is solely due to the circular scale:

\(0 + 0.52\, \text{mm} = 0.52\, \text{mm}\)

Converting \(0.52\, \text{mm}\) to centimeters (since the options are in cm):

\(0.52\, \text{mm} = 0.052\, \text{cm}\)

Therefore, the diameter of the wire is \(0.052\, \text{cm}\).

Thus, the correct answer is 0.052 cm.