Question

A student performs an experiment for determination of ` g [ = ( 4 pi^(2) L)/(T^(2)) ] , L ~~ 1m` , and he commits an error of `Delta L`. For `T` he takes the time of `n` oscillations with the stop watch of least count ` Delta T` . For which of the following data , the measurement of `g` will be most accurate ?
A. `DeltaL =0.5,DeltaT =0.1, n =20`
B. `DeltaL =0.5, DeltaT =0.1, n =50`
C. `DeltaL = 0.5 DeltaT = 0.01, n = 20`
D. `DeltaL = 0.1DeltaT = 0.05, n=50`

Answer 1

`(Deltag)/(g) = (DeltaL)/(L) + 2(DeltaT)/(T)`
In option `(D)` error in `Deltag` is minimum and number of repetition of measurement are maximum In this case the error in g is minimum .