First slide

Elastic behaviour of solids

Question

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

Moderate

A

1:1
B

1:2
C

1:3
D

1:4

Solution

$Y = \frac{Fl}{aΔl}$
In the given problem, $Y, l and Δl$ are constants.
$∴ F \propto a$
$or F \propto {πr}^{2} or F \propto r^{2} or \frac{F_{1}}{F_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} = \frac{1}{4}$

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