Question

The head scale of the screw gauge has $200$ divisions and its thimble moves by $0.5\,mm$ along the main scale for one complete rotation of the screw. Find its least count.
A. $0.00025$
B. $0.005$
C. $0.025$
D. $0.0025$

Answer 1

Screw gauge has a U-shaped metal frame $M$ whose one end $Q$ is fixed by a metal piece and other end $P$ is attached to a cylindrical hub $H$. Hub has millimeters and half millimeters depending upon the pitch of the screw; this is the linear scale.

Complete step by step answer:
A nut is threaded in the hub and the end $P$ of the metal frame through which a screw moves.A cap which is hollow and cylindrical also rotates when the screw goes in and out. The surface of the cap is divided into hundred equal parts; this scale is circular scale.

Least count is defined as the minimum distance we can measure by an instrument.
Least count of screw gauge $= \dfrac{{{\text{Pitch}}}}{{{\text{Number of division on circular scale}}}}$
As given in above question: Thimble moves (pitch) $= 0.5mm$
Divisions on head scale $= 200$
Using the formula of least count:
$L.C. = \dfrac{{0.5}}{{200}}$
$\therefore L.C. = 0.00025$

Hence, option A is the correct answer.

Note: When we change the sense of rotation suddenly from either clockwise to anticlockwise or vice versa the head of screw moves but the screw may not move which results in changed readings. This happens due to wear and tear of threading because of prolonged use and loose fitting. To overcome this problem screws should always be rotated in the same sense of rotation.