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Standard IX

Physics

Vernier Caliper

The least cou...

Question

The least count of a vernier callipers is 0.01 cm. It has an error of +0.02 cm while measuring the radius of a cylinder. The main scale reading is 3.60 cm and the 8th vernier scale division coincides with main scale, then what will be the correct radius of the cylinder?

1.72

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1.75

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1.83

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1.87

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Solution

The correct option is B 1.83
L.C. $=$ 0.01 cm
Error $=$ + 0.02 cm $\Rightarrow$ Positive zero
error $=$ + 0.02 cm
main scale reading (MSR) $=$ 3.60 cm 8 $^{t h}$ vernier scale coincides with main scale
$\Rightarrow$ vernier coincidence (VC) $=$ 8
We know that
Correct diameter $=$ [main scale reading+ (L.C $\times$ V.C)] - (error)
$=$ [3.60 + (0.01 $\times$ 8)] - [+ 0.002]
$=$ (3.60 + 0.08)- (+0.02)
$=$ 3.68 - 0.02
$=$ 3.66 cm
$∴ c o r r e c t r a d i u s = \frac{d i a m e t e r}{2} = \frac{3.66}{2}$
$= 1.83 c m$

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