First slide

Hook's Law

Question

Two wires of same material have lengths l and 2l. Their radii are in the ratio 1 : 2. The wires are stretched by the same force. If elongation produced in the second wire is 1 mm, then elongation in the first wire will be

Easy

A

6 mm
B

4 mm
C

3 mm
D

2 mm

Solution

(4)
$\begin{array}{l} E l o n g a t i o n δ = \frac{F l}{A γ} = \frac{F l}{π σ^{2} γ} \\ ∴ \frac{δ_{1}}{δ_{2}} = \frac{l_{1}}{l_{2}} {(\frac{r_{2}}{r_{1}})}^{2} = (\frac{1}{2}) {(2)}^{2} = 2 \\ ∴ δ_{1} = 2 δ_{2} = 2 \times 1 m m = 2 m m . \end{array}$

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