Units and Measurements Part 1

Given, 9 divisions of main scale are equal to 10 divisions of Vernier scale. i.e. 9 MSD = 10 VSD $\Rightarrow VSD=\frac{9}{10} MSD$ ...(i) Size of 1 main scale division, 1 MSD = 1 mm Now, least count, LC = 1MSD − 1VSD ...(ii) Using Eqs. (i) and (ii), we get $LC=1 MSD-\frac{9}{10} MSD=\frac{1}{10} MSD=\frac{1}{10} \mathrm{mm}$ While measuring the diameter of bob. Main Scale Reading, MSR = 10 mm Vernier Scale Reading, VSR = 8 Zero error, e = 0.04 cm Now, diameter, $d=[MSR+LC \times VSR]-e$ $=\left(10 \mathrm{mm}+\frac{1}{10} \times 8 \mathrm{mm}\right)-0.04 \mathrm{cm}$ $=(10.8) \mathrm{mm}-0.04 \mathrm{cm}$ $=1.08 \mathrm{cm}-0.04 \mathrm{cm}=1.04 \mathrm{cm}$ Radius, $r=\frac{d}{2}=\frac{1.04}{2} \mathrm{cm}=0.52 \mathrm{cm}=52 \times 10^{-2} \mathrm{cm}$ ∴ Correct answer is 52.