JEE Mains · Physics · STD 11 - 1. units,dimensions and measurement
One main scale division of a vernier callipers is \(a\) \(cm\) and \(n ^{\text {th }}\) division of the vernier scale coincide with \(( n -1)^{\text {th }}\) division of the main scale. The least count of the callipers in \(mm\) is
- A \(\frac{10 na }{( n -1)}\)
- B \(\frac{10 a }{( n -1)}\)
- C \(\left(\frac{ n -1}{10 n }\right) a\)
- D \(\frac{10 a }{ n }\)
Answer & Solution
Correct Answer
(D) \(\frac{10 a }{ n }\)
Step-by-step Solution
Detailed explanation
\((n-1) a=n\left(a^{\prime}\right)\) \(a^{\prime}=\frac{(n-1) a}{n}\) \(\therefore L \cdot C \cdot=1 M S D-1 VSD\) \(=\left(a-a^{\prime}\right) c m\) \(=a-\frac{(n-1) a}{n}\) \(=\frac{n a-n a+a}{n}=\frac{a}{n} c m\) \(=\left(\frac{10 a}{n}\right) m m\)
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