Experimental Physics

JEE Main level, single correct, medium

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Question 11 of 70

One main scale division of a vernier caliper is equal to mm units. If nth \mathrm{n}^{\text {th }} division of main scale coincides with (n+1)th (n+1)^{\text {th }} division of vernier scale, the least count of the vernier caliper is :

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Answer: (C) m(n+1)\frac{m}{(n+1)}

nMSD=(n+1)VSD⇒1VSD=nn+1MSDL⋅C=1MSD−1VSDL⋅C=m−m(nn+1)L⋅C=m(n+1−nn+1)⇒L⋅C=(mn+1)\begin{aligned} & \mathrm{n} M S D=(\mathrm{n}+1) \mathrm{VSD} \\ & \Rightarrow 1 \mathrm{VSD}=\frac{\mathrm{n}}{\mathrm{n}+1} \mathrm{MSD} \\ & \mathrm{L} \cdot \mathrm{C}=1 \mathrm{MSD}-1 \mathrm{VSD} \\ & \mathrm{L} \cdot \mathrm{C}=\mathrm{m}-\mathrm{m}\left(\frac{\mathrm{n}}{\mathrm{n}+1}\right) \\ & \mathrm{L} \cdot \mathrm{C}=\mathrm{m}\left(\frac{\mathrm{n}+1-\mathrm{n}}{\mathrm{n}+1}\right) \\ & \Rightarrow \mathrm{L} \cdot \mathrm{C}=\left(\frac{\mathrm{m}}{\mathrm{n}+1}\right)\end{aligned}

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