Two wires of the same length and same material but radii in the ratio of $1 : 2$ are stretched by unequal forces to produce equal elongation. The ratio of the two forces is

1 : 1

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1 : 2

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1 : 3

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1 : 4

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Solution

The correct option is C $1 : 4$
$Y = \frac{F l}{a △ l}$
In the given problem, $Y, l$ and $△ l$ are constants.
$△ F \propto a$
or $F \propto π r^{2}$ or $F \propto r^{2}$ or $\frac{F_{1}}{F_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{1}{4}$ .

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Two wires of the same length and same material but radii in the ratio of 1:2 are stretched by unequal forces to produce equal elongation. The ratio of the two forces is

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The correct option is C $1 : 4$
$Y = \frac{F l}{a △ l}$
In the given problem, $Y, l$ and $△ l$ are constants.
$△ F \propto a$
or $F \propto π r^{2}$ or $F \propto r^{2}$ or $\frac{F_{1}}{F_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{1}{4}$ .