The diameter of a spherical bob is measured using a vernier callipers. 9 divisions of the main scale, in the vernier callipers, are equal to 10 divisions of vernier scale. One main scale division is 1 mm. The main scale reading is 10 mm and 8ᵗʰ division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of 0.04 cm, then the radius of the bob is ___________ × 10⁻² cm.

Solution

Physics sir · 4 steps

Find the least count, take the reading, subtract the zero error, and only then halve it for the radius.

1. Least count. 10 vernier divisions equal 9 main scale divisions, so 1 VSD = 0.9 mm. The least count is 1 MSD - 1 VSD = 1 - 0.9 = 0.1 mm = 0.01 cm.
2. Observed reading. Main scale reading is 10 mm = 1.0 cm. The 8th vernier division coincides, so add 8 × 0.01 = 0.08 cm. The observed diameter is 1.08 cm.
3. Remove zero error. A positive zero error means the instrument reads too much, so subtract it.

   D = 1.08 cm - 0.04 cm = 1.04 cm

4. So. The radius is 1.04/2 = 0.52 cm = 52 × 10⁻² cm, so the answer is 52.

The common slip: 104. Stopping at the corrected diameter gives 104. The question asks for the radius, so divide 1.04 cm by 2.

The idea to keep. Correct reading = MSR + (coinciding division × LC) minus zero error. A positive zero error is always subtracted. Fix the diameter first, then convert to radius.

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