When a spring is stretched by $2\, cm$, it stores $100 \,J$ of energy. If it is stretched further by $2 \,cm$, the stored energy will be increased by ............. $\mathrm{J}$
When a spring is stretched by $2\, cm$, it stores $100 \,J$ of energy. If it is stretched further by $2 \,cm$, the stored energy will be increased by ............. $\mathrm{J}$
$100$
$200$
$300$
$400$
When a spring is stretched by $2\, cm$, it stores $100 \,J$ of energy. If it is stretched further by $2 \,cm$, the stored energy will be increased by ............. $\mathrm{J}$
$100 = \frac{1}{2}k{x^2}$ (given)
$W = \frac{1}{2}k(x_2^2 - x_1^2) = \frac{1}{2}k[{(2x)^2} - {x^2}]$
$ = 3 \times \left( {\frac{1}{2}k{x^2}} \right) = 3 \times 100 = 300\,J$
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