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Law of Conservation of Energy

When two spri...

Question

When two springs A and B with force constant $K_{A} a n d K_{B}$ are stretched by same force,the respective work done on them is:

K_{B} : K_{A}

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K_{A} : K_{B}

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K_{A} K_{B} : 1

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\sqrt K_4 : \sqrt K_B

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Solution

The correct option is A $K_{B} : K_{A}$
It is given that two springs A and B are there.

Work done on first spring $W_{1} = \frac{1}{2} K_{A} x_{1}^{2} . . . . . . . . . (1)$

Work done on second spring $W_{2} = \frac{1}{2} K_{B} x_{2}^{2} . . . . . . . . . . (1)$

Since, force is same $F = K_{A} x_{1} = K_{B} x_{2} . . . . . . . . . (3)$

Taking ratios of equation (1) and (2)
$\frac{W_{1}}{W_{2}} = \frac{K_{A} x_{1}^{2}}{K_{B} x_{2}^{2}} = \frac{F x_{1}}{F x_{2}} = \frac{K_{B}}{K_{A}} (f r o m (1))$

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