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8. mechanical properties of solids — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics8. mechanical properties of solids1 Mark
MCQ
Wires $A$ 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
    $2:3$
  • ✓
    $3:4$
  • C
    $3:2$
  • D
    $6:1$
✓

Answer

Correct option: B.
$3:4$
b
(b) $U = \frac{1}{2}Fl = \frac{{{F^2}L}}{{2AY}}$. $U \propto \frac{L}{{{r^2}}}$ $(F$ and $Y$ are constant$)$

$\frac{{{U_A}}}{{{U_B}}} = \left( {\frac{{{L_A}}}{{{L_B}}}} \right) \times {\left( {\frac{{{r_A}}}{{{r_B}}}} \right)^2}$= $(3) \times {\left( {\frac{1}{2}} \right)^2} = \frac{3}{4}$

 

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