In a screw gauge, the zero of the circular scale lies 3 divisions above the horizontal pitch line when their metallic studs are brought in contact. Using this instrument thickness of a sheet is measured. If pitch scale reading is 1 mm and the circular scale reading is 51 then the correct thickness of the sheet is ____ mm.
[Assume least count is 0.01 mm ]

Solution

Physics sir · 3 steps

Circular zero above the line means a negative zero error, so add 0.03 mm back to the reading.

1. Sign of zero error. With the studs touching, the circular zero sits 3 divisions above the pitch line. So the zero has not come down to the line, and the line sits at division 97 instead of 0. The gauge reads less than the true value, so the zero error is negative: -3 × 0.01 = -0.03 mm.
2. Observed reading. Pitch scale reading plus circular scale reading times least count: 1 + 51 × 0.01 = 1.51 mm.

   True reading = Observed - Zero error = 1.51 - (-0.03) = 1.54 mm

3. So. The correct thickness of the sheet is 1.54 mm, option (a).

The idea to keep. Circular zero above the line gives a negative zero error, and below the line gives a positive one. Always subtract the zero error with its sign: true = observed minus zero error.

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