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
⇒VSD=

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=1‌MSD−

9

10

‌MSD=

1

10

‌MSD=

1

10

‌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×VSR]−e
=(10‌mm+

1

10

×8‌mm)−0.04‌cm
=(10.8)‌mm−0.04‌cm
=1.08‌cm−0.04‌cm=1.04‌cm
Radius, r=

d

2

=

1.04

2

‌cm=0.52‌cm=52×10−2‌cm
∴ Correct answer is 52.