question_answer

A uniform dense rod with non-uniform Young's modulus is hanging from ceiling under gravity. If elastic energy density at every point is same, then Young's modulus with x will change in which of the shown graph.  

A)

B)       

C)

D)       

Correct Answer: C

Solution :

[c] Elastic energy density at \[A=\frac{1}{2}\frac{{{(stress)}^{2}}}{Y}=\] constant \[\frac{1}{2}\frac{{{\left( \frac{M}{L}\frac{x}{A}g \right)}^{2}}}{Y}=\]constant        \[Y\propto {{x}^{2}}\]