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  4. Two wires of same material and length are stretched by the same force. Their masses are in the ratio 4:3 . The ratio of their elongation will be

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Q. Two wires of same material and length are stretched by the same force. Their masses are in the ratio $ 4:3 $ . The ratio of their elongation will be

MGIMS WardhaMGIMS Wardha 2015

Solution:

$ Y=\frac{Fl}{A\Delta l} $ Here $ y,l $ and F are constant So, $ \Delta l\propto \frac{1}{A} $ Also $ m=(V)\rho =(Al)\rho $ i.e. $ m\propto A $ $ \therefore $ $ \Delta l\propto \frac{1}{m} $ $ \Rightarrow $ $ \frac{\Delta {{l}_{1}}}{\Delta {{l}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}=\frac{3}{4} $ $ (\because {{m}_{1}}:{{m}_{2}}=4:3) $