A mass of 5 kg is connected to a spring. The potential energy curve… | JEE Main 2021 (1 Sep, Shift 2)

Q68JEE Main 2021 · 1 SEP · SHIFT 2Medium

Spring Systems

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?

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Answer: (c)

From the graph, equilibrium at $x = 2$ m and $U = 10$ J at the turning points, so $A = 2$ m.
$\frac{1}{2}kA^2 = 10 \Rightarrow \frac{1}{2}k(2)^2 = 10 \Rightarrow k = 5\text{ N/m}$
$T = 2\pi\sqrt{\frac{m}{k}} = 2\pi\sqrt{\frac{5}{5}} = 2\pi\text{ s}$
Pendulum: $2\pi\sqrt{\frac{4}{g}} = 2\pi \Rightarrow g = 4\text{ m/s}^2$
So the answer is (c) 4 m/s $^2$ .

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