In an experiment for determining the gravitational acceleration $g$ of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure. What is the value of $g$ at the place? ...... $m/s^2$
JEE MAIN 2014, Medium
Download our app for free and get started
From graph it is clear that wher
$\mathrm{L}=1 \mathrm{m}, \mathrm{T}^{2}=4 \mathrm{s}^{2}$
As we know,
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$
$\Rightarrow \mathrm{g}=\frac{4 \pi^{2} \mathrm{L}}{\mathrm{T}^{2}}$
$=4 \times\left(\frac{22}{7}\right)^{2} \times \frac{1}{4}=\left(\frac{22}{7}\right)^{2}$
$\therefore \mathrm{g}=\frac{484}{49}=9.87 \mathrm{m} / \mathrm{s}^{2}$
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
- 1The equation of a simple harmonic motion is $X = 0.34\cos (3000t + 0.74)$ where $X$ and $t$ are in $mm$ and $sec$. The frequency of motion isView Solution
- 2View SolutionIn forced oscillations, a particle oscillates simple harmonically with a frequency equal to
- 3For a particle showing motion under the force $F=-5(x-2)^2$, the motion is .......View Solution
- 4View SolutionAn assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. At this instant, the springs are relaxed. The left mass is displaced to the/left and theiright mass is displaced to the right by same distance and released. The resulting collision is elastic. The time period of the oscillations of system is
- 5A plate oscillated with time period $‘T’$. Suddenly, another plate put on the first plate, then time periodView Solution
- 6A spring hangs vertically from the ceiling and a mass is attached to its free end. When the mass is pulled down and released, it oscillates vertically with simple harmonic motion of period $T$ . The variation with time $t$ of its distance from the ceiling is as shown. Which statement gives a correct deduction from this graph?View Solution
- 7View SolutionA simple pendulum is vibrating in an evacuated chamber, it will oscillate with
- 8A particle executes $SHM$ on a straight line path. The amplitude of oscillation is $2\, cm.$ When the displacement of the particle from the mean position is $1\, cm,$ the numerical value of magnitude of acceleration is equal to the numerical value of magnitude of velocity. The frequency of $SHM$ (in $second^{-1}$) is :View Solution
- 9A spring is stretched by $5 \,\mathrm{~cm}$ by a force $10 \,\mathrm{~N}$. The time period of the oscillations when a mass of $2 \,\mathrm{~kg}$ is suspended by it is :(in $s$)View Solution
- 10A simple pendulum oscillates freely between points $A$ and $B$. We now put a peg (nail) at the point $C$ as shown in above figure. As the pendulum moves from $A$ to the right, the string will bend at $C$ and the pendulum will go to its extreme point $D$. Ignoring friction, the point $D$View Solution
