Question 55: Properties of Matter

Question

A wire of length $$L$$ and radius $$r$$ is clamped at one end. If its other end is pulled by a force $$F$$, its length increases by $$l$$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

Accepted Answer

$$\begin{aligned}
& Y=\frac{	ext { stress }}{	ext { strain }} \
& Y=\frac{\frac{\mathrm{F}}{\frac{\pi \mathrm{r}^2}{\ell}}}{\frac{\ell}{\mathrm{L}}}
\end{aligned}$$
$$\mathrm{F}=\mathrm{Y} \pi \mathrm{r}^2 	imes \frac{\ell}{\mathrm{L}} \quad 	ext{.... (i)}$$
$$\begin{aligned}
& \mathrm{Y}=\frac{\frac{\mathrm{F} / 2}{\pi \mathrm{r}^2 / 4}}{\frac{\Delta \ell}{\mathrm{L}}} \
& \mathrm{F}=\mathrm{Y} \frac{\Delta \ell}{\mathrm{L}} 	imes 2 	imes \frac{\pi \mathrm{r}^2}{4}
\end{aligned}$$
From (i)
$$\begin{aligned}
& \mathrm{Y} \pi \mathrm{r}^2 \frac{\ell}{\mathrm{L}}=\mathrm{Y} \frac{\Delta \ell}{\mathrm{L}} \frac{\pi \mathrm{r}^2}{2} \
& \Delta \ell=2 \ell
\end{aligned}$$

Answer

2 times

Answer

4 times

Answer

3 times

Answer

$$\frac{3}{2}$$ times

Properties of Matter

A wire of length $L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

Choose the correct answer: