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Mechanical Properties of Solids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMechanical Properties of Solids1 Mark
MCQ
Wire $A$ and $B$ are made from the same material $A$ has twice the diameter and three times the length of $B$. If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in $A$ to that in $B$ is:
  • A
    $2 : 3$
  • ✓
    $12 : 1$
  • C
    $3 : 2$
  • D
    $6 : 1$
✓

Answer

Correct option: B.
$12 : 1$
Given $D_A=2 D ; I_A=3 I, D_B=D, I_B=I$
$F_A=F=F_B, Y_A=Y_B=Y$
Energy stored $(E) =\frac{1}{2}\times\frac{(\text{Stress})^2}{\text{Y}}\times\text{Volume}$
$\therefore\text{E}_\text{A}=\frac{\frac{\text{F}}{\pi}(2\text{D})^2}{\text{Y}}\times\frac{\pi(2\text{D})^2}{4}\times3\text{l}$
$\text{E}_\text{B}=\frac{1}{2}\frac{\frac{\text{F}}{\pi}\text{D}^2}{\text{Y}}\times\frac{\pi\text{D}^2}{4}\times\text{l}$
$\frac{\text{E}_\text{A}}{\text{E}_\text{B}}=\frac{12}{1}$

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