Question

11. A student measures the distance traversed in freefall of a body, initially at rest in a given time. Heuses this data to estimate g, the acceleration dueto gravity. If the maximum percentage errors inmeasurement of the distance and the time are e,and e, respectively, the percentage error in theestimation of g is ​

Answer 1

time taken by a body to reach ground during free fall is:

t=√(2h/g)

so g=2h/t²

apply log on both sides,

log(g)=log(2)+log(h)-2log(t)

differentiate on both sides,

dg/g=dh/h-2dt/t

multiply by 100 on both sides,

100dg/g=100dh/h-200dt/t

given |100dh/h|=|100dt/t|=e

so maximum percentage error is:

dg/g%=e+2e=3e

max percentage error in g is 3g