Question

The diameter of a cylinder is measured using a Vernier calipers 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

• A. 5.112 cm
• B. 5.124 cm
• C. 5.136 cm
• D. 5.148 cm

Answer 1

The correct option is B

5.124 cm

We can see that 1 MSD = 0.05 cms given("It is found that the zero of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale."), vernier scale has 50 divisions equivalent 2.45 cm.

No. of MSD in 2.45 cms = $\frac{2.45}{0.05}$ = 49

$\therefore$ 50 VSD = 49 MSD

$\Rightarrow$ 1 VSD = $\frac{49}{50}$MSD

Least count = 1 MSD - 1 VSD = 1 MSD - $\frac{49}{50}$MSD

=$\frac{1}{50}$MSD

=$\frac{1}{50}\times 0.05$cms

= 0.001 cms

Final reading = MSR + L.C$\times$ VSR

= 5.10 + 0.001$\times$24

= 5.124 cms