JEE Main 2024 · Physics · Fluid Mechanics, Elasticity and Surface Tension · easy

A steel wire of length 2 m and cross-sectional area 1 mm^2 is stretched by hanging a 10 kg mass from it. Young's modulus of steel is 2×10^11 N m^-2…

Numerical answer

A steel wire of length

2\ \mathrm{m}

and cross-sectional area

1\ \mathrm{mm^2}

is stretched by hanging a

10\ \mathrm{kg}

mass from it. Young's modulus of steel is

2\times10^{11}\ \mathrm{N\,m^{-2}}

and

g=10\ \mathrm{m\,s^{-2}}

. The elastic potential energy stored in the wire (in mJ) is

Show answer and solution

Answer: 50

The tension is

F=mg=100\ \mathrm{N}

. Extension

\Delta L=\dfrac{FL}{AY}=\dfrac{100\times2}{10^{-6}\times2\times10^{11}}=10^{-3}\ \mathrm{m}

. Stored energy

U=\tfrac12F\,\Delta L=\tfrac12(100)(10^{-3})=0.05\ \mathrm{J}=50\ \mathrm{mJ}

. Equivalent:

U=\tfrac12\times\text{stress}\times\text{strain}\times\text{volume}

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