In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by 0.5 mm on a complete rotation. For a particular observation the reading on the main scale is 5 mm and the 20ᵗʰ division of the circular scale coincides with reference line. Calculate the true reading.

Solution

Physics sir · 4 steps

Find the least count, read the instrument, then take the zero error away from the reading.

1. Least count. One full turn moves the screw 0.5 mm, and that turn is split into 50 circular divisions. So each division is 0.5/50 = 0.01 mm.
2. Zero error. With the jaws closed the reading should be zero, but the 5th division sits on the reference line. That is a positive zero error of 5 × 0.01 = +0.05 mm. The gauge reads too high by this amount.
3. Observed reading. Main scale reading plus circular scale reading: 5 + 20 × 0.01 = 5.20 mm.

   True reading = Observed - Zero error = 5.20 - 0.05 = 5.15 mm

4. So. The true reading is 5.15 mm, option (c).

The idea to keep. Zero error is what the gauge shows when it should show nothing. Always subtract it, with its sign, from every reading: true = observed minus zero error.

Answer from the NTA final answer key. Solution by PrepWiser.