Solveeit Logo
Login

Question

Question: (i) Define the least count of an instrument. (ii) What is the least count of a standard laborator...

(i) Define the least count of an instrument.
(ii) What is the least count of a standard laboratory micrometer screw gauge?

Explanation

Solution

Least count is the lowest limit of measuring using any measuring instrument. It represents the accuracy of measurement and it is the difference between the value of main scale division and auxiliary scale division. The Least count of a measuring instrument is the smallest and accurate value in the measuring quantity. The least count of a standard laboratory micrometer screw gauge is0.001cm0.001cm.

Formula used:
Least count of a screw gauge is given as:
LC = pitch of the mirrortotal number of circular scale division{\text{LC = }}\dfrac{{{\text{pitch of the mirror}}}}{{{\text{total number of circular scale division}}}}

Complete step by step solution:
(i)Least Count of an Instrument:
The least count of a measuring instrument is the smallest and accurate value in the measured quantity that can be resolved on the instrument's scale. The least count is calculated by dividing the main scale reading with the total number of divisions on the secondary scale. It represents the accuracy of measurement.

(ii)The least count of a standard laboratory screw gauge:
We know, Least count of a screw gauge is given as:
LC = pitch of the mirrortotal number of circular scale division{\text{LC = }}\dfrac{{{\text{pitch of the mirror}}}}{{{\text{total number of circular scale division}}}}
The distance traveled in one whole rotation in the main scale division is called the pitch of the micrometer.
In the standard laboratory, Pitch = 1$$$$mm= 0.1$$$$cm.
The number of circular scale divisions, N = 100100.
Putting all in the equation, we get:
L.C = \dfrac{{0.1}}{{100}}$$$$cm=0.0010.001.cmcm
So, the least count of a standard laboratory micrometer screw gauge is0.001cm0.001cm.

Note:
The least count is the capability of an instrument to measure minimum distance accurately.
A screw gauge is used to measure the diameter of the thin wires and the thickness of the small glass, sheets, and plastic.
A screw gauge of 100100 divisions will move the cap scale along the main scale by 1100\dfrac{1}{{100}}of mm-0.010.01 mm.
The least count is defined as the ratio between the pitch of the screw and the number of divisions on the circular scale.