Question

If the energy stored in spring '$\text{A}$' is $20\text{J}$, then energy stored in spring '$\text{B}$' is (under the same stretching force)

• A. $10\text{J}$
• B. $25\text{J}$
• C. $40\text{J}$
• D. $35\text{J}$

Answer 1

The correct option is C $40\text{J}$

Let $E_A=$ Energy stored in spring $\text{A}$
$E_B=$ Energy stored in spring $\text{B}$
$x_A=$ Displacement of spring $\text{A}$
$x_B=$ Displacement of spring $\text{B}$

Then, $E_B=\frac{1}{2}k{x}_B^2=\frac{1}{2}k\times {\left(\frac{F}{k}\right)}^2$
$=\frac{F^2}{2k}$ ... (i)
& $E_A=\frac{1}{2}\times 2k\times x_A^2=\frac{1}{2}\times 2k\times {\left(\frac{F}{2k}\right)}^2$
$=\frac{F^2}{4k}$ ... (ii)

Dividing (i) by (ii):
$\frac{E_B}{E_A}=\frac{\frac{F^2}{2K}}{\frac{F^2}{4K}}=2$
$\Rightarrow \frac{E_B}{20}=2\Rightarrow E_B=40\text{J}$