Question

If the energy stored in spring $A=10\text{J}$, then energy stored in $B$ is (under same stretching force)

• A. $10\text{J}$
• B. $5\text{J}$
• C. $2.5\text{J}$
• D. $1.25\text{J}$

Answer 1

The correct option is B $5\text{J}$

It is given that, energy stored in the spring $A$ is $E_A=\frac{1}{2}k{x}_A^2$, $(x_A=\frac{F}{K}$)

Energy stored in spring $\left(E_B\right)=\frac{1}{2}\left(K_{spring,B}\right)\times \left(x_B^2\right)$ where $K_{spring,B}=2K$
$x_B=\left(\frac{F}{2K}\right)$
$\therefore E_B=\frac{1}{2}\times 2K\times {\left(\frac{F}{2K}\right)}^2=\frac{1}{2}\times (\frac{1}{2}\times K\times {\left(\frac{F}{K}\right)}^2)$
$\because \left(E_A\right)=(\frac{1}{2}\times K\times {\left(\frac{F}{K}\right)}^2)$
$\Rightarrow E_B=\frac{1}{2}\times \left(E_A\right)=\frac{1}{2}\times 10\text{J}$
$\Rightarrow E_B=5\text{J}$

Hence option B is the correct answer.