Question

Rewrite the following equation in terms of $A$:

$n=\frac{1}{2\pi }\sqrt{\frac{8T}{lA}}$

• A. $A=\frac{2T}{l{\pi }^2{n}^2}$
• B. $A=\frac{T}{l{\pi }^2{n}^2}$
• C. $A=\frac{2T}{l{\pi }^{2}n}$
• D. none of these

Answer 1

Answer: (A)

$A=\frac{2T}{l{\pi }^2{n}^2}$

$n=\frac{1}{2\pi }\sqrt{\frac{8T}{lA}}$
Taking square on both sides, we get
$n^2=\frac{1}{4{\pi }^2}\left(\frac{8T}{lA}\right)$
$4{\pi }^2{n}^{2}Al=8T$
$\therefore A=\frac{2T}{l{\pi }^2{n}^2}$