Question

While measuring the inner diameter and outer diameter of a hollow tube to determine its thickness by using a Vernier callipers, the main scale readings are found to be 20 mm and 60 mm respectively. What are the minimum and maximum possible thickness if one main scale = 1 mm, number of Vernier scale division = 10?

• A. 39.1 mm, 40.25 mm
• B. 60 mm, 90 mm
• C. 20.9 mm, 21.45 mm
• D. 19.5 mm, 20.45 mm

Answer 1

The correct option is A 39.1 mm, 40.25 mm

$\begin{array}{c}\text{Inner}\\ MSR=20mm\\ lMSD=\mathrm{lmm}\\ \text{Coinciding division be n,}\\ n\text{belongs to}0-10\end{array}$

$\begin{array}{c}\text{Outer}\\ MSR=60mm\\ \text{1 MSD =}1mm\\ \text{Coinciding division be m}\\ \text{m belongs to 0 - 10}\end{array}$

$\begin{array}{c}\text{Let least count be}K\\ \text{Outer diameter}=60+mK\\ \text{Inner diameter}20+nK\\ \text{Thickness}=40+(m-n)k\end{array}$

$\begin{array}{c}\text{If}m>n\text{then thickess}\\ \text{is sligtly greater than}40.\\ \text{If}m<n\text{then thickness}\\ \text{is s lightiy less then}40.\\ \text{Only option (A) satifies the}\\ \text{above condition.}\end{array}$