Question

Given that:
$T=2\pi \sqrt{\frac{I}{g}}$ , express g in terms of $T$ , $\pi$ and $I$.

Answer 1

We have,

$T=2\pi \sqrt{\frac{I}{g}}$

On squaring both sides, we get

$T^2={\left(2\pi \sqrt{\frac{I}{g}}\right)}^2$

$T^2=4{\pi }^2\times \frac{I}{g}$

$\frac{T^2}{4{\pi }^2}=\frac{I}{g}$

$\frac{T^2}{4{\pi }^{2}I}=\frac{1}{g}$

$g=\frac{4{\pi }^{2}I}{T^2}$

Hence, this is the answer.