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Potential Energy Formulae

Two springs P...

Question

Two springs P and Q of force constant $k_{p}$ and $k_{Q} (k_{Q} = \frac{k_{p}}{2})$ are stretched by applying forces of equal magnitude. If the energy stored in Q is E, then the energy stored in P is?

A

E/2

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B

2E

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C

E

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D

E/4

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Solution

The correct option is A E/2
We know,

Potential Energy $= \frac{1}{2} k x^{2} = \frac{F^{2}}{2 k}$

i.e $P E \propto \frac{1}{k}$

$\frac{P E_{P}}{P E_{Q}} = \frac{K_{Q}}{k_{P}}$

$P E_{P} = \frac{E}{2}$

Option $A$ is the correct answer

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