Question

If $T=2\pi \sqrt{\frac{L}{g}}$, then ‘L’ is equal to

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

Answer 1

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


$T=2\pi \sqrt{\frac{L}{g}}$
$\sqrt{\frac{L}{g}}=\frac{T}{2\pi }$
$\Rightarrow$ Squaring both sides,
$\frac{L}{g}=\frac{T^2}{(2\pi {)}^2}$
$L=\frac{T^{2}g}{4{\pi }^2}$