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A steel wire is 1m long and $1 m m^{2}$ in area of cross-section. If it takes 200 N to stretch this wire by 1mm how much force will be required to stretch the wire of the same area and of same material having length of 10m to 1002 cm

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100 N

200 N

2000 N

400 N

answer is C.

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Detailed Solution

$Y = \frac{F L}{A e}$

$F \propto \frac{e}{ℓ} \Rightarrow \frac{F_{1}}{F_{2}} = \frac{e_{1}}{e_{2}} \times \frac{ℓ_{2}}{ℓ_{1}}$

$\frac{200}{F_{2}} = \frac{10^{- 3}}{0.02} \times \frac{10}{1}$

$F_{2} = 400 N$

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