The diameter of a spherical bob is measured using a vernier...

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

1mm .

The main scale reading is

10mm

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 . 04cm,

then the radius of the bob is _____________

\times {10}^{- 2}cm .

Correct answer

Step-by-step solution

$9MSD = 10VSD$
$1VSD = 0 . 9mm$
$1MSD = 1mm$
$∴ L . C . = \dfrac{MSD - VSD}{MSD} = \dfrac{1 - 0 . 9}{1} = 0 . 1$
Reading = Main scale reading $+$ L.C. $\times$ vernier scale reading
$= 10 + \left(0 . 1 \times 8\right)$
$= 10 . 8mm$

Reading of diameter $= 10 . 8mm - 0 . 4mm = 10 . 4mm$
radius of the bob $= 5 . 2mm$
$= 0 . 52cm = 52 \times {10}^{- 2}cm$

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