Question

A solid metal bar of uniform diameter D and length L is hang vertically from a ceiling. If the density of the material of the bar is $\rho$ and the modulus of elasticity is E, then the total elongation of the bar due to its own weight is

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

Answer 1

The correct option is B $\frac{\rho L^2}{2E}$

The elongation of bar due to its own weight (W) is

$\Delta =\frac{WL}{2AE}$

Now, $W=\rho AL$

$\therefore \Delta =\frac{\rho L^2}{2E}$