Discussion Forum



1)

The increase  in energy of a metal bar of length L and  cross-sectional area A when   compressed with a load M along its length is (where, Y= Young's modulus of the material of metal bar )


A) $\frac{FL}{2 AY}$

B) $\frac{F^{2}L}{2 AY}$

C) $\frac{F^{}L}{2AY}$

D) $\frac{F^{2}L^{2}}{2 AY}$

Answer:

Option B

Explanation:

Energy = $\frac{1}{2}$ x stress x strain x volume

 =  $\frac{1}{2}\frac{(stress)^{2}}{Y}\times volume$

 =$\frac{1}{2}\frac{(\frac{F}{A})^{2}}{Y}\times L A$  [ as stress = F/A, volume = L x A]

 or energy (E)= $\frac{F^{2}L}{2 AY}$