Two wires of the same material have masses in the ratio 3:4 . The ratio of their extensions under the same load if their lengths are in the ratio 9:10 is

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27 : 40

6 : 5

5 : 3

27 : 25

answer is D.

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Detailed Solution

$Y = \frac{F ℓ}{A e} \Rightarrow Y = \frac{F ℓ^{2}}{A ℓ e} = \frac{F ℓ^{2}}{V e} = \frac{d F ℓ^{2}}{m e}$

$e \propto \frac{ℓ^{2}}{m} \Rightarrow \frac{e_{1}}{e_{2}} = {(\frac{ℓ_{1}}{ℓ_{2}})}^{2} \frac{m_{2}}{m_{1}} = {(\frac{9}{10})}^{2} \frac{4}{3} = \frac{81}{100} \times \frac{4}{3} = \frac{27}{25}$

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