Question

acceleration due to gravity is measured on the surface of the earth by using simple pendulum.if alpha and beta are relative errors in measurements of length and time period respectively then percentage error in the measurement of acceleration due to gravity is

Answer 1

{alpha +2 beta }×100

Answer 2

$\bold{(a+2 b) 100 \%}$ is the percentage error that we get when the acceleration due to gravity on the surface of the earth.

Important steps  

The relative error in length measurement is given as follows  

$\frac{\Delta L}{L}=\mathrm{a}$ { here ∆L is the change in length or error in length}

$\frac{\Delta T}{T}=\mathrm{b}$ { here ∆T is the change in time period or error in time period}

$\frac{\Delta g}{g}=\frac{\Delta L}{L}+2 \times \frac{\Delta T}{T}$

 $a + 2b$

Hence percentage error that we get in g is given by $(a+2 b) 100 \%$