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=0.5 ,DeltaT=0.05,n=50`

Answer 1

Correct Answer - D
`(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.