Question 271: Units , Dimensions and Error Analysis

Question

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero
of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions
equivalent to 2.45 cm. The 24
th
division of the Vernier scale exactly coincides with one of the main scale
divisions. The diameter of the cylinder is

Accepted Answer

From the given data :
One main scale division (MSD) is $ 5.15 	ext{ cm} - 5.10 	ext{ cm} = 0.05 	ext{ cm} $.
One Vernier scale division (VSD) is $ \frac{2.45 	ext{ cm}}{50} = 0.049 	ext{ cm} $.
The least count (LC) of the Vernier calipers is:
$$ 	ext{LC} = 1 	ext{ MSD} - 1 	ext{ VSD} = 0.05 	ext{ cm} - 0.049 	ext{ cm} = 0.001 	ext{ cm} $$
Given the main scale reading (MSR) is 5.10 cm and the Vernier scale reading (VSR) is 24. The diameter $ D $ of the cylinder is calculated as:
$$ \begin{aligned} D & = 	ext{MSR} + 	ext{VSR} 	imes 	ext{LC} \\   & = 5.10 	ext{ cm} + 24 	imes 0.001 	ext{ cm} \\   & = 5.124 	ext{ cm} \end{aligned} $$

Answer

5.112 cm

Answer

5.124 cm

Answer

5.136 cm

Answer

5.148 cm

Units , Dimensions and Error Analysis

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