Question

A spherometer has 10 threads per cm and its circular scale has 50 divisions. The least count of the instrument is
$\begin{align}
  & A.0.01cm \\
 & B.0.02cm \\
 & C.0.002cm \\
 & D.0.2cm \\
\end{align}$

Answer 1

Hint: A spherometer is an instrument used for the measurement of the radius of the curvature of a sphere or curved surface. It has on the plane scale, you can call it the main scale and a circular scale. While doing measurement you have to move the central screw and measurement is done depending upon the position of the screw. First, calculate the pitch of the screw which is the distance between two consecutive threads on the screw. In one complete rotation of the circular scale, the screw is moved by a distance equal to one pitch. Therefore, the least count of spherometer is the ratio of pitch of the screw to the total number of divisions on the circular scale.

Formula used:
$\text{Pitch =}\dfrac{\text{Distance moved by screw}}{\text{Number of complete rotations}}$
\[\text{Least count of spherometer = }\dfrac{\text{pitch of the spherometer screw}}{\text{Number of divisions on circular scale}}\]

Complete step by step answer:
A spherometer is an instrument used for the measurement of the radius of the curvature of a sphere or curved surface. Its working is based on the principle of a micrometer screw. It has a tripod frame with three supporting legs. These three legs form an equilateral triangle. It also has a central screw which can be moved in a perpendicular direction. Depending upon how much this screw is moved we can measure the thickness or radius of curvature of curved surfaces.
The pitch of the screw is defined as the distance moved by the screw in one complete rotation of a circular scale.
$\text{Pitch =}\dfrac{\text{Distance moved by screw}}{\text{Number of complete rotations}}$
The pitch of a spherometer is also defined as the distance between two consecutive threads of the spherometer screw.
Given that, a spherometer has 10 threads per cm, therefore, the distance between two consecutive threads of the screw and hence the pitch is given as
$\text{Pitch =}\dfrac{\text{1cm}}{\text{10}}=0.1cm$
The least count of the spherometer is the smallest measurement done by it.
The least count of the spherometer can be calculated a\[\text{Least count of spherometer = }\dfrac{\text{pitch of the spherometer screw}}{\text{Number of divisions on circular scale}}\]
Given that there are 50 divisions on the circular scale.
Therefore,
\[\text{Least count of spherometer = }\dfrac{\text{0}\text{.1cm}}{50}=0.002cm\]

Answer - C. 0.002cm

Note:
The least count of any instrument is the smallest measurement that can be measured by that instrument. So in this case the least count of spherometer is 0.002cm which means we cannot take measurements smaller than 0.002cm. The least count of an instrument is related to the precision of that instrument.