In an Spectrometer experiment, the angles are required to be measured using vernier callipers .29 divisions of the main scale exactly coincide with 30 divisions of the Vernier scale. If the smallest division of the main scale is half a degree ( 0.5°), then the least count of the instrument is

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Half minute

One degree

One minute

Half degree

answer is A.

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Detailed Solution

$LC = \frac{M . S . D}{n} = \frac{0 {.05}^{\circ}}{30} = \frac{1^{0}}{60} = 1 \min or$
In spectrometer main scale 360º divided in 720 divisions 1 div $= \frac{1}{2} = 0 {.5}^{\circ} = 30^{'}$
$\begin{array}{l} 30 V = 29 S \Rightarrow V = \frac{29}{30} S \\ S - V = S - \frac{29}{30} S = \frac{1}{30} S \\ S - V = \frac{1}{30}, but 1 S = 30^{'} Hence least count = 1^{'} \end{array}$

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