Two springs of force constants $300\, N / m$ (Spring $A$) and $400$ $N / m$ (Spring $B$ ) are joined together in series. The combination is compressed by $8.75\, cm .$ The ratio of energy stored in $A$ and $B$ is $\frac{E_{A}}{E_{B}} .$ Then $\frac{E_{A}}{E_{B}}$ is equal to
AIIMS 2019, Diffcult
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Consider the spring $A$ is compressed by $x$ and spring $B$ is
compressed by $(8.75-x)$
The compressed force is,
$F=k x$
$F=300 x=400(8.75-x)$
On solving the above equation,
$x=5 \,cm$
Spring $B$ is compressed by $(8.75-5)=3.75 cm$
Now,
$\frac{E_{A}}{E_{B}}=\frac{\frac{1}{2} k_{A} x_{A}^{2}}{\frac{1}{2} k_{B} x_{B}^{2}}$
$=\frac{\frac{1}{2} \times 300 \times 5^{2}}{\frac{1}{2} \times 400 \times 3.75^{2}}$
$=\frac{4}{3}$
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