First slide

Elastic Modulie

Question

Two wires of same length and same material but of radii r and 2r are stretched by forces F and f respectively to produce equal elongation. The ratio F to f is

Moderate

A

1 : 1
B

1 : 2
C

2 : 1
D

1 : 4

Solution

Given, $r_{1} = r, r_{2} = 2 r$
Now, we know that, $Y = \frac{F}{A} \cdot \frac{l}{Δ l} = \frac{F}{π r^{2}} \cdot \frac{l}{Δ l}$
So, $\frac{F}{π r_{1}^{2}} = \frac{f}{π r_{2}^{2}}$ $(∵ l, Δ l and Y are same)$
$\Rightarrow \frac{F}{f} = \frac{r_{1}^{2}}{r_{2}^{2}} \Rightarrow \frac{F}{f} = \frac{r^{2}}{4 r^{2}} \Rightarrow \frac{F}{f} = \frac{1}{4}$

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