Question

A solid metal bar of uniform sectional area throughout its length hangs vertically from its upper end. Details of the bar are :
Length = 6 m, material density = 8 x ${10}^5$ N/mm${}^3$ and E = 2 x 10${}^5$ N/mm${}^2$. What will be the total elongation of the bar in mm ?

• A. $\frac{288}{{10}^4}$
• B. $\frac{48}{{10}^4}$
• C. $\frac{144}{{10}^4}$
• D. $\frac{72}{{10}^4}$

Answer 1

The correct option is D $\frac{72}{{10}^4}$

Total elongation of the bar will be
$\Delta L=\frac{\gamma L^2}{2E}=\frac{8\times {10}^{-5}\times (6\times 1000{)}^2}{2\times 2\times {10}^5}$
$=\frac{72}{{10}^4}mm$