Question

A wire of length 2m is made from 10 cm³ of copper. A force F is applied so that its length increases by 2 mm. Another wire of length 8 m is made from the same volume of copper. If the force F is applied to it, its length will increase by

• A. 0.8 cm
• B. 1.6 cm
• C. 2.4 cm
• D. 3.2 cm

Answer 1

Answer: (D)

3.2 cm

Answer 2

$l = \frac{FL}{AY} = \frac{FL^{2}}{VY}$ $\mathbf{\therefore}\mathbf{l}\mathbf{\propto}\mathbf{L}^{\mathbf{2}}$ [As V, Y and F are constant]

$\frac{l_{2}}{l_{1}} = \left\lbrack \frac{L_{2}}{L_{1}} \right\rbrack^{2} = \left( \frac{8}{2} \right)^{2} = 16$ ⇒ l₂ = 16 l₁ = 16 × 2 mm = 32 mm = 3.2 cm