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  4. Two springs of force constant 1000 N/m and 2000 N/m are streched by same force. The ratio of their respective potential energies is

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Q. Two springs of force constant 1000 N/m and 2000 N/m are streched by same force. The ratio of their respective potential energies is

MGIMS WardhaMGIMS Wardha 2009

Solution:

Forces are same $ \therefore $ $ \frac{{{k}_{1}}{{x}_{1}}}{{{k}_{2}}{{x}_{2}}}=1 $ $ \Rightarrow $ $ \frac{{{k}_{1}}}{{{k}_{2}}}=\frac{{{x}_{2}}}{{{x}_{1}}} $ $ \frac{{{x}_{2}}}{{{x}_{1}}}=\frac{1000}{2000}=\frac{1}{2} $ $ \frac{{{U}_{1}}}{{{U}_{2}}}=\frac{\frac{1}{2}{{k}_{1}}x_{1}^{2}}{\frac{1}{2}{{k}_{2}}x_{2}^{2}}=\frac{{{k}_{1}}}{{{k}_{2}}}{{\left[ \frac{{{x}_{1}}}{{{x}_{2}}} \right]}^{2}} $ $ =\frac{1}{2}\times 4=\frac{2}{1}=2:1 $