Question

Energy stored in spring $A=20\text{J}$, then energy stored in spring $B$ is (under same extension of the spring)

• A. $20\text{J}$
• B. $30\text{J}$
• C. $40\text{J}$
• D. $50\text{J}$

Answer 1

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

Let, $E_A$ = Energy stored in spring ${}^{\prime }{A}^{\prime }$
$E_B$ = Energy stored in spring ${}^{\prime }{B}^{\prime }$
$K_1$ = spring constant for spring ${}^{\prime }{A}^{\prime }$
$K_2$ = spring constant for spring ${}^{\prime }{B}^{\prime }$

We know that spring potential energy $E=\frac{1}{2}k{x}^2=\frac{Fx}{2}$

Hence, $E_B=\frac{2Fx}{2}=Fx...\left(i\right)$ As, for the same extension, $x_A=x_B=x$ , $(F_B=2F)$

Given that energy stored in the spring $A$ is $20\text{J}$
$E_A=\frac{Fx}{2}=20\text{J}...\left(ii\right)$ $(F_A=F)$

Dividing $\left(ii\right)$ by $\left(i\right)$, we get
$\frac{E_A}{E_B}=\frac{\frac{F.x}{2}}{F.x}$

$\Rightarrow \frac{E_A}{E_B}=\frac{1}{2}$

$\Rightarrow \frac{20}{E_B}=\frac{1}{2}$
$\Rightarrow E_B=40\text{J}$

Hence option C is the correct answer