Mechanical Properties of Solids - Result Question 7
8. Two wires A and B are of the same material. Their lengths are in the ratio $1: 2$ and the diameter are in the ratio $2: 1$. If they are pulled
by the same force, then increase in length will be in the ratio
(a) $2: 1$
(b) $1: 4$
(c) $1: 8$
(d) $8: 1$
[1988]
Topic 2: Bulk and Rigidity Modulus & Work Done in Stretching a Wire
Show Answer
Solution:
- (c) We know that Young’s modulus
$Y=\frac{F}{\pi r^{2}} \times \frac{L}{\ell}$
Since Y, F are same for both the wires, we have, $\ell \propto \frac{L}{r^{2}}$
or, $\frac{\ell_1}{\ell_2}=\frac{r_2^{2} \times L_1}{r_1^{2} \times L_2}=\frac{(D_2 / 2)^{2} \times L_1}{(D_1 / 2)^{2} \times L_2}$
or, $\frac{\ell_1}{\ell_2}=\frac{D_2^{2} \times L_1}{D_1^{2} \times L_2}=\frac{D_2^{2}}{(2 D_2)^{2}} \times \frac{L_2}{2 L_2}=\frac{1}{8}$
So, $\quad \ell_1: \ell_2=1: 8$
