Question # What is the fractional error in ( g ) calculated from

# What is the fractional error in ( g ) calculated from

( mathrm{T}=2 pi sqrt{ell / mathrm{g}} ? ) Given that fractional errors in ( mathrm{T} ) and

( ell ) are ( pm mathrm{x} ) and ( pm mathrm{y} ) respectively.

(1) ( x+y )

(2) ( x-y )

(3) ( 2 x+y )

( (4) 2 x-y )

Solution

( begin{aligned} T^{2} &=4 pi^{2} frac{1}{9} g &=54 pi frac{21}{T^{2}} g & alpha frac{1}{T 2} frac{Delta g}{g} &=frac{Delta 1}{1}+2 frac{Delta T}{T} &=theta+2 x &=y+2 x &=(3) text { option } end{aligned} )