Question

What is the fractional error in $g$ calculated from $T=2\pi\sqrt{\frac{l}{g}}$ if it is given that fractional errors in $T$ and $l$ are $\pm x$ and $\pm y$, respectively?

• A. $x+y$
• B. $x-y$
• C. $2x+y$
• D. $(2x-y)$

Answer 1

Answer: (C)

$2x+y$

Answer 2

$g=\frac{4\pi^{2}l}{T^{2}}$ $\Rightarrow \frac{\Delta g}{g}=\frac{\Delta l}{l}+2\frac{\Delta T}{T}$ $\Rightarrow \frac{ \Delta g}{g}=y+2x$