Question

A student measure the diameter of a small steel ball using a screw gauge of least count $0.001cm$. The main scale reading is $10mm$ and with ${25}^{th}$ divisions coincides with reference line. The correct diameter of the ball is (Number of circular scale division is $50$)

• A. $1.35cm$
• B. $1.25cm$
• C. $1.025cm$
• D. $1.42cm$

Answer 1

The correct option is C $1.025cm$

$\begin{array}{c}L\cdot C=0.001cm\\ \text{i.e. least count}\\ M\cdot S\cdot R=10mm=1cm\\ \text{i.e. main scale reading}\\ {25}^{\text{th}}\text{division coincides with}\\ \text{reference line .}\end{array}$

$\begin{array}{c}\text{C.S.R}=25\times LC\\ =0.025cm\\ \\ \text{Final reading}\\ =M.S\cdot R+C\cdot S\cdot R\\ =1+0.025\\ =1.025cm\end{array}$