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Standard XII

Physics

Young's Modulus of Elasticity

A uniform alu...

Question

A uniform aluminium wire of length $3$ m and area of cross-section $2$ $m m^{2}$ is extended through $12 m m$ . The energy stored in the wire is ___________. ( $Y_{A l} = 7 \times 10^{10} N / m^{2}$ )

336 J

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33.6 J

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3.36 J

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0.336 J

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Solution

The correct option is C $3.36 J$
$A =$ area of cross section
$L =$ length of the wire
$K =$ spring constant

$K = \frac{A Y_{a l}}{L} E = \frac{1}{2} K x^{2} = \frac{A Y_{a l} x^{2}}{2 L} = \frac{2 \times 10^{- 6} \times 7 \times 10^{10} \times {(12 \times 10^{- 3})}^{2}}{2 \times 3} = 3.36 J$

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A uniform aluminium wire of length 3m and area of cross-section 2 mm2 is extended through 12 mm. The energy stored in the wire is ___________. (YAl=7×1010N/m2)

The correct option is C 3.36 JA= area of cross sectionL= length of the wireK= spring constant K=AYalLE=12Kx2=AYalx22L=2×10−6×7×1010×(12×10−3)22×3=3.36J

A uniform aluminium wire of length $3$ m and area of cross-section $2$ $m m^{2}$ is extended through $12 m m$ . The energy stored in the wire is ___________. ( $Y_{A l} = 7 \times 10^{10} N / m^{2}$ )

The correct option is C $3.36 J$
$A =$ area of cross section
$L =$ length of the wire
$K =$ spring constant

$K = \frac{A Y_{a l}}{L} E = \frac{1}{2} K x^{2} = \frac{A Y_{a l} x^{2}}{2 L} = \frac{2 \times 10^{- 6} \times 7 \times 10^{10} \times {(12 \times 10^{- 3})}^{2}}{2 \times 3} = 3.36 J$