Question

A bar of circular cross-section varies uniformly from a cross-section 2D to D. If extension of the bar is calculated treating it as a bar of average diameter, then the percentage error will be

• A. 10
• B. 25
• C. 33.33
• D. 50

Answer 1

The correct option is A 10

${\Delta }_o=\frac{4PL}{\pi E{D}_1{D}_2}$

Actual extension,

${\Delta }_o=\frac{4PL}{\pi \left(2D^2\right)E}=\frac{2PL}{\pi D^{2}E}$

The average diameter of bar
$=\frac{2D+D}{2}=1.5D$

Approximate extension,
$\Delta =\frac{4PL}{\pi \times (1.5D{)}^{2}E}=\frac{4PL}{2.25\pi D^{2}E}$
$\therefore$ $Errorincalculation=(1-\frac{\Delta }{{\Delta }_o})\times 100$
$=(1-\frac{2}{2.25})\times 100=11.11\%=10\%$