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?
Select the correct option:
A
$10 \mathrm{~m} / \mathrm{s}^2$ (
B
$5 \mathrm{~m} / \mathrm{s}^2$
C
$4 \mathrm{~m} / \mathrm{s}^2$
D
$9.8 \mathrm{~m} / \mathrm{s}^2$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
From potential energy curve
$$
\begin{aligned}
& U_{\max }=\frac{1}{2} k A^2 \Rightarrow 10=\frac{1}{2} k(2)^2 \\
& \Rightarrow k=5
\end{aligned}
$$
Now $T_{\text {spring }}=T_{\text {pendulum }}$
$$
\begin{aligned}
& 2 \pi \sqrt{\frac{5}{5}}=2 \pi \sqrt{\frac{4}{g}} \\
& \Rightarrow i=\sqrt{\frac{4}{g}} \Rightarrow g=4 \text { on planet }
\end{aligned}
$$
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