Question

A wire of length $L$ and radius $r$ is fixed at one end. When a stretching force $F$ is applied at free end, the elongation in the wire is $l$. When another wire of same material but of length $2L$ and radius $2r$, also fixed at one end is stretched by a force $2F$ applied at free end, then elongation in the seconds wire will be

• A. $l/2$
• B. $l$
• C. $2l$
• D. $l/4$

Answer 1

Answer: (B)

$l$

Young's modulus of a material is given by:

$Y=\frac{FL}{A\Delta L}$

$=\frac{FL}{\pi r^{2}l}...........\left(i\right)$

In the second case, young's modulus remains the same. Hence,

$Y=\frac{F^{\prime }{L}^{\prime }}{A^{\prime }\Delta L^{\prime }}$

$=\frac{2F\times 2L}{\pi (2r{)}^2\times \Delta L^{\prime }}$

$=\frac{FL}{\pi r^2\Delta L^{\prime }}..............\left(ii\right)$

From (i) & (ii), $\Delta L^{\prime }=l$