What is the fractional error in g calculated from T=2π√(l/g) if it is given that fractional errors in T and l are ± x and ± y, respectively?

Question

What is the fractional error in g calculated from T=2π√(l/g) if it is given that fractional errors in T and l are ± x and ± y, respectively? (A) x+y (B) x-y (C) 2x+y (D) (2x-y)

Tardigrade Admin · Accepted Answer

g=(4π2l/T2) ⇒ (Δ g/g)=(Δ l/l)+2(Δ T/T) ⇒ ( Δ g/g)=y+2x

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

$x + y$

$x - y$

$2 x + y$

$(2 x - y)$

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

Q. What is the fractional error in g calculated from T=2πgl​​ if it is given that fractional errors in T and l are ±x and ±y, respectively?

x+y

x−y

2x+y

(2x−y)