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The 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. - Physics

Short Note

The 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.

 
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Solution

Given : 

\[\text{ Elastic limit of steel } \frac{F}{A} = 8 \times {10}^5 \text{ N/ m}^2 \]
\[\text{ Young's modulus of steel Y }= 2 \times {10}^{11} \text{ N/ m}^2 \]
\[\text{ Length of steel wire L } = \frac{1}{2}\text{ m = 0 . 5 m }\]

The elastic limit of steel indicates the maximum pressure that steel can bear.
Let the maximum elongation of steel wire be \[∆ L\] .

\[Y = \frac{F}{A} \frac{L}{∆ L}\]
\[ \Rightarrow ∆ L = \frac{FL}{AY}\]
\[ \Rightarrow ∆ L = \frac{8 \times {10}^5 \times \left( 0 . 5 \right)}{2 \times {10}^{11}}\]
\[ = 2 \times {10}^{- 3} \text{ m = 2 mm }\]

Hence, the required elongation of steel wire is 2 mm.

 

 

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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 14 Some Mechanical Properties of Matter
Q 3 | Page 300
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