Question

A circular rod which tapers uniformly from 30 mm diameter to 20 mm diameter and another rectangular bar of constant thickness 5 mm and uniformly tapering in width from 20 mm to 10 mm. The length and applied axial load are same for both the bars, the ratio of the elongation in the respective bar is ? (Take $E=2\times {10}^{5}N/m{m}^2$ for both material)

• A. $0.25$
• B. $0.15$
• C. $0.50$
• D. $6.67$

Answer 1

The correct option is B $0.15$

Extension of uniformly tapering circular rod due to axial load=

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

$=\frac{4\times P\times L}{\pi \times 2\times {10}^5\times 30\times 20}$

Extension of uniformly tapering rectangular bar

$=\frac{PL}{Et(B_1-B_2)}lo{g}_e\left(\frac{B_1}{B_2}\right)$

$=\frac{PL}{2\times {10}^5\times 5(20-10)}\times lo{g}_e\left(\frac{20}{10}\right)$

$\text{Required ratio}=\frac{\frac{4PL}{\pi E\times 30\times 20}}{\frac{PL}{Et(20-10)lo{g}_e\left(2\right)}}$

$=\frac{4}{\pi \times 30\times 20}\times \frac{5\times 10}{lo{g}_e\left(2\right)}=0.153$