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
Download our app for free and get started
From potential energy curve
${U}_{\max }=\frac{1}{2} {kA}^{2} \Rightarrow 10=\frac{1}{2} {k}(2)^{2}$
$\Rightarrow {k}=5$
Now ${T}_{\text {spring }}={T}_{\text {pendulum }}$
$2 \pi \sqrt{\frac{5}{5}}=2 \pi \sqrt{\frac{4}{g}}$
$\Rightarrow 1=\sqrt{\frac{4}{g}} \Rightarrow g=4 \text { on planet }$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1Two identical pendulums oscillate with a constant phase difference $\frac{\pi}{4}$ and same amplitude. If the maximum velocity of one is $v$, the maximum velocity of the other will be ........View Solution
- 2The variation of the acceleration $a$ of the particle executing $S.H.M.$ with displacement $x$ is as shown in the figureView Solution
- 3Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two motions is $.....(degree)$View Solution
- 4A particle of mass m is under the influence of a force $F$ which varies with the displacement $x$ according to the relation $F = - kx + {F_0}$ in which $k$ and ${F_0}$ are constants. The particle when disturbed will oscillateView Solution
- 5If two similar springs each of spring constant $K _{1}$ are joined in series, the new spring constant and time period would be changed by a factorView Solution
- 6Two pendulums differ in lengths by $22\,cm$ . They oscillate at the same place such that one of them makes $15\,oscillations$ and the other makes $18\,oscillations$ during the same time. The lengths (in $cm$ ) of the pendulums areView Solution
- 7A cuboidal piece of wood has dimensions $a, b$ and $c$. Its relative density is $d$. It is floating in a large body of water such that side a is vertical. It is pushed down a bit and released. The time period of $SHM$ executed by it is :View Solution
- 8View SolutionFor a particle executing simple harmonic motion, which of the following statements is not correct
- 9If $< E >$ and $< U >$ denote the average kinetic and the average potential energies respectively of mass describing a simple harmonic motion, over one period, then the correct relation isView Solution
- 10View SolutionA graph of the square of the velocity against the square of the acceleration of a given simple harmonic motion is