A) 2 : 1
B) 1 : 2
C) 4 : 1
D) 1 : 4
Correct Answer: A
Solution :
Forces are same \[\therefore \] \[\frac{{{k}_{1}}{{x}_{1}}}{{{k}_{2}}{{x}_{2}}}=1\] \[\Rightarrow \] \[\frac{{{k}_{1}}}{{{k}_{2}}}=\frac{{{x}_{2}}}{{{x}_{1}}}\] \[\frac{{{x}_{2}}}{{{x}_{1}}}=\frac{1000}{2000}=\frac{1}{2}\] \[\frac{{{U}_{1}}}{{{U}_{2}}}=\frac{\frac{1}{2}{{k}_{1}}x_{1}^{2}}{\frac{1}{2}{{k}_{2}}x_{2}^{2}}=\frac{{{k}_{1}}}{{{k}_{2}}}{{\left[ \frac{{{x}_{1}}}{{{x}_{2}}} \right]}^{2}}\] \[=\frac{1}{2}\times 4=\frac{2}{1}=2:1\]
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