A) \[E\]
B) \[2E\]
C) \[\frac{E}{8}\]
D) \[\frac{E}{4}\]
E) \[\frac{E}{2}\]
Correct Answer: E
Solution :
Given: \[{{k}_{p}}=2{{k}_{Q}}\] By stretching spring energy given \[E=\frac{1}{2}k{{x}^{2}}\] \[[\because F=kx]\] Or \[E=\frac{1}{2}\frac{{{F}^{2}}}{k}\] For spring P \[{{E}_{p}}=\frac{1}{2}\frac{{{F}^{2}}}{{{k}_{p}}}\] For spring Q \[{{E}_{Q}}=\frac{1}{2}\frac{{{F}^{2}}}{{{k}_{Q}}}\] \[\therefore \] \[\frac{{{E}_{P}}}{{{E}_{Q}}}=\frac{{{k}_{Q}}}{{{k}_{P}}}=\frac{1}{2}\] Or \[{{E}_{P}}=\frac{{{k}_{Q}}}{2}=\frac{E}{2}\]You need to login to perform this action.
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