Oscillations

JEE Main level, single correct, medium

86 of 194

Question 86 of 194

A mass of 5kg5kg 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 4m4m 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: (A) 4ms−24m{s}^{-2}

From the figure, A=2mA=2m
12mω2A2=10\dfrac{1}{2}m{\omega }^{2}{A}^{2}=10
12mω2(2)2=10\dfrac{1}{2}m{\omega }^{2}(2{)}^{2}=10
mω2=5m{\omega }^{2}=5
5(ω2)=55\left({\omega }^{2}\right)=5
ω2=1{\omega }^{2}=1
ω=1\omega =1
T=2πω=2πT=\dfrac{2\pi }{\omega }=2\pi
2πℓgp=2π2\pi \sqrt{\dfrac{\ell }{{g}_{p}}}=2\pi
2π4gp=2π2\pi \sqrt{\dfrac{4}{{g}_{p}}}=2\pi
gp=4m/s2{g}_{p}=4m/{s}^{2}

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