Question

In the formula $T=2\pi \sqrt{\frac{L}{g}},\pi$ and $g$ are constants. If we solve the formula for $L$

• A. $\frac{Tg}{2\pi }$
• B. $\frac{T{g}^2}{2\pi }$
• C. $\frac{T^2}{4{\pi }^{2}g}$
• D. $\frac{T^2}{4\pi g^2}$
• E. $\frac{g{T}^2}{4{\pi }^2}$

Answer 1

The correct option is E $\frac{g{T}^2}{4{\pi }^2}$

Given $T=2\pi \sqrt{\frac{L}{g}}$
Now square it on both sides

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

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