Question

A 200 mm sine bar is used for the measurement of angle of a component as ${25}^{\circ }$. If the error in length of sine bar is 5 microns, the error in the measurement of angle is

• A. 0.76''
• B. 2.4''
• C. 0.31''
• D. 1.3''

Answer 1

The correct option is B 2.4''

L=200 mm,

$\theta ={20}^{\circ }$

$dL=5\mu m$

$d\theta =\tan \theta [\frac{\text{dh}}{h}-\frac{\text{dL}}{L}]$

$d\theta =\tan \theta [0-\frac{dL}{L}]$

$d\theta =\tan {25}^{\circ }\left[\frac{-5\times {10}^{-6}}{200\times {10}^{-3}}\right]$

$d\theta =1.16\times {10}^{-5}$

$d\theta =1.16\times {10}^{-5}\times \frac{180}{\pi }\times 3600$

$={2.39}^{\prime \prime }\approx {2.4}^{\prime \prime }$