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  4. 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 ?

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Q. 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 ?Physics Question Image

JEE MainJEE Main 2014Oscillations

Solution:

$T =2 \pi \sqrt{\frac{\ell}{ g }} $
$T ^{2}=4 \pi^{2} \frac{\ell}{ g }$
$g =4 \pi^{2} \frac{\ell}{ T ^{2}} $
$T ^{2}=\frac{4 \pi^{2}}{ g }$
$\frac{4 \pi^{2}}{ g }=4 $
$g =\pi^{2}=9.87$