NEET-XII-Physics
14: Some Mechanical Properties of Matter
- #3The elastic limit of steel is 8 × 108 N m-2 and its Young modulus 2 × 1011 N m-2. Find the maximum elongation of a half-metre steel wire that can be given without exceeding the elastic limit.Ans : Given:
`` \,\mathrm{\,Elastic\,}\,\mathrm{\,limit\,}\,\mathrm{\,of\,}\,\mathrm{\,steel\,}\frac{F}{A}=8\times {10}^{5}\,\mathrm{\,N\,}/{\,\mathrm{\,m\,}}^{2}``
`` \,\mathrm{\,Young\,}\text{'}\,\mathrm{\,s\,}\,\mathrm{\,modulus\,}\,\mathrm{\,of\,}\,\mathrm{\,steel\,}Y=2\times {10}^{11}\,\mathrm{\,N\,}/{\,\mathrm{\,m\,}}^{2}``
`` \,\mathrm{\,Length\,}\,\mathrm{\,of\,}\,\mathrm{\,steel\,}\,\mathrm{\,wire\,}L=\frac{1}{2}\,\mathrm{\,m\,}=0.5\,\mathrm{\,m\,}``
`` ``
The elastic limit of steel indicates the maximum pressure that steel can bear.
Let the maximum elongation of steel wire be `` ∆L``.
`` Y=\frac{F}{A}\frac{L}{∆L}``
`` \Rightarrow ∆L=\frac{FL}{AY}``
`` \Rightarrow ∆L=\frac{8\times {10}^{5}\times \left(0.5\right)}{2\times {10}^{11}}``
`` =2\times {10}^{-3}\,\mathrm{\,m\,}=2\,\mathrm{\,mm\,}``
Hence, the required elongation of steel wire is 2 mm.
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