Question 9: Units , Dimensions and Error Analysis

Question

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{	ext {th }}$ Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has

Accepted Answer

When the jaws are fully closed, the zero of the Vernier scale is shifted to the right of the zero of the main scale.
This means the Vernier caliper has a
positive zero error
.
Now let us find its magnitude.
Given:
$1$ main scale division $= 1 \, 	ext{mm}$
Total Vernier divisions $= 10$
For a standard Vernier calipers:
$$ 10 \, 	ext{VSD} = 9 \, 	ext{MSD} $$
So,
$$ 1 \, 	ext{VSD} = \frac{9}{10} \, 	ext{MSD} $$
Since
$$ 1 \, 	ext{MSD} = 1 \, 	ext{mm} $$
therefore,
$$ 1 \, 	ext{VSD} = 0.9 \, 	ext{mm} $$
Hence the least count is
$$ 	ext{L.C.} = 1 \, 	ext{MSD} - 1 \, 	ext{VSD} = 1 - 0.9 = 0.1 \, 	ext{mm} $$
Now, it is given that the $7^	ext{th}$ Vernier division coincides with a main scale division.
So zero error
$$ = 7 	imes 	ext{L.C.} = 7 	imes 0.1 = 0.7 \, 	ext{mm} $$
Convert into cm:
$$ 0.7 \, 	ext{mm} = 0.07 \, 	ext{cm} $$
Since the zero of Vernier scale is to the right, the zero error is
positive
.
Therefore, the Vernier caliper has
$$ \boxed{0.07 \, 	ext{cm positive zero error}} $$
So, the correct option is
Option C
.

Answer

0.07 cm negative zero error

Answer

0.7 cm negative zero error

Answer

0.07 cm positive zero error

Answer

0.7 cm positive zero error

Units , Dimensions and Error Analysis

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