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 solve the given problem, we need to calculate the diameter of the wire using a screw gauge with the provided readings and calibrations.

1. Main Scale Reading (MSR): The given main scale reading is \(0\, \text{mm}\).
2. Circular Scale Reading (CSR): The circular scale reading is \(52\) divisions.
3. Calibration Detail: We know that \(1\, \text{mm}\) on the main scale corresponds to \(100\) divisions on the circular scale. Therefore, each division on the circular scale represents \(0.01\, \text{mm}\) (since \(\frac{1\, \text{mm}}{100}\)).
4. Calculate the Total Reading:
   • The circular scale reading (CSR) gives us \(52\) divisions, which is equivalent to \(52 \times 0.01\, \text{mm} = 0.52\, \text{mm}\).
5. Total Diameter of the Wire:
   • Adding the main scale reading (MSR) and the effective circular scale reading, the total diameter is: \(0 \, \text{mm} + 0.52\, \text{mm} = 0.52\, \text{mm}\).
   • Converting this to centimeters: \(0.52\, \text{mm} = 0.052\, \text{cm}\).

Therefore, the diameter of the wire is \(0.052\, \text{cm}\). This corresponds to the correct answer given in the options:

0.052 cm