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 $8^{\text{th}}$ 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 ______ $\times 10^{-2} \mathrm{~cm}$.

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Units & Measurement

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

8^{th}

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 ______

\times 1 0^{- 2} cm

Answer: 52

Solution

Ten vernier divisions equal nine main-scale divisions, so

1 VSD = 0.9

mm and the least count is

1 - 0.9 = 0.1

mm. The reading is the main-scale value plus the coinciding division times the least count:

10 + 8 (0.1) = 10.8

mm. The positive zero error

0.04

= 0.4

mm is subtracted, giving a true diameter

10.8 - 0.4 = 10.4

= 1.04

cm. The radius is half of this,

0.52

cm, that is

52 \times 1 0^{- 2}

cm.

JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Integer answer

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JEE Main · 2021 · 31 Aug 2021 · Shift 2 · Units & Measurement

Solution

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