A mass of $5\, {kg}$ is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length $4\, {m}$ has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed? (In ${m} / {s}^{2}$)
JEE MAIN 2021, Diffcult
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From potential energy curve
${U}_{\max }=\frac{1}{2} {kA}^{2} \Rightarrow 10=\frac{1}{2} {k}(2)^{2}$
$\Rightarrow {k}=5$
Now ${T}_{\text {spring }}={T}_{\text {pendulum }}$
$2 \pi \sqrt{\frac{5}{5}}=2 \pi \sqrt{\frac{4}{g}}$
$\Rightarrow 1=\sqrt{\frac{4}{g}} \Rightarrow g=4 \text { on planet }$
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