Question

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree (= 0.5 degrees) then the least count of the instrument is:A. one minute
B. half minuteC. one degree
D. half degree

Answer 1

Final Answer : A :1 minute


Steps:
1) We have,
Least Count of Main Scale ( in degree)
= 0.5° =1°/2

2) According to the question,
29 divisions of the main Scale coincide with 30 divisions on Vernier.
=> 29 MSD = 30 VSD

3) We know ,
Least Count, LC = 1 MSD - 1 VSD
= 1 MSD - 29/30 MSD
=1/30 MSD
=1/30*1/2° =1°/60
=1' = 1 minute

Hence, Least Count of Instrument is 1 minute.

Answer 2

Steps:

1) We have,

Least Count of Main Scale ( in degree)

= 0.5° =1°/2

2) According to the question,

29 divisions of the main Scale coincide with 30 divisions on Vernier.

=> 29 MSD = 30 VSD

3) We know ,

Least Count, LC = 1 MSD - 1 VSD

= 1 MSD - 29/30 MSD

=1/30 MSD

=1/30*1/2° =1°/60

=1' = 1 minute