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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
A wire of length $2\, m$ is made from $10\;c{m^3}$ of copper. A force $F$ is applied so that its length increases by $2\, mm.$ Another wire of length 8 m is made from the same volume of copper. If the force $F$ is applied to it, its length will increase by......... $cm$
  • A
    $0.8$
  • B
    $1.6$
  • C
    $2.4$
  • ✓
    $3.2$
✓

Answer

Correct option: D.
$3.2$
d
(d) $l = \frac{{FL}}{{AY}} = \frac{{F{L^2}}}{{(AL)Y}} = \frac{{F{L^2}}}{{VY}}$

$l \propto {L^2}$ If volume of the wire remains constant

$\frac{{{l_2}}}{{{l_1}}} = {\left( {\frac{{{L_2}}}{{{L_1}}}} \right)^2} = {\left( {\frac{8}{2}} \right)^2} = 16$

${l_2} = 16 \times {l_1} = 16 \times 2 = 32mm = 3.2cm$

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