The diameter of a wire is measured with a screw gauge having...

The diameter of a wire is measured with a screw gauge having 50 divisions on circular scale and by one complete rotation of circular scale, main scale moves $0.5 \mathrm{~mm}$. If reading of screw gauge is $0.250 \mathrm{~cm}$. The minimum percentage error in the reading will be (A) $0.4$ (B) $0.8$ (C) 4 (D) 5

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Key Concepts

Percentage Error

Percentage error quantifies the error in a measurement relative to the true value, expressed as a percentage. It is computed by dividing the absolute error (often the least count for precise instruments) by the measured value and then multiplying by 100.

Measurement Uncertainty

Measurement uncertainty refers to the doubt that exists about the result of any measurement. In precision instruments like screw gauges, this is often taken as the least count, representing the smallest possible error in the measurement.

Screw Gauge

A screw gauge is a precision instrument used to measure small lengths or diameters with high accuracy. It works on the principle of converting the rotational motion of a screw into linear motion, and its design includes a main scale and a circular scale that allow for fine measurements.

Least Count

The least count of an instrument is the smallest measurement that can be reliably read from it. In a screw gauge, it is determined by dividing the movement corresponding to one complete turn of the circular scale by the number of divisions on that scale, indicating the resolution of the instrument.

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