Question

A solid uniform metal bar of diameter D mm and length $lmm$ hangs vertically from its upper end, The density of the material is $pN/m{m}^3$ and its modulus of elasticity is $EN/m{m}^2$, The total extension of the rod due to its own weight would be

• A. $\frac{\rho l^2}{2E}$
• B. $\frac{\rho l}{2E}$
• C. $\frac{\rho l}{4E}$
• D. $\frac{\rho l^2}{4E}$

Answer 1

The correct option is A $\frac{\rho l^2}{2E}$

The expansion of a prismatic bar due to self,
$\Delta =\frac{\rho l^2}{2E}=\frac{Wl}{2AE}$
$\rho =$ Specific weight of material
$W=$ Total weight of bar