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 ?

Options

A. `Delta l 5 mm` `Delta T 0.2 s` `n 10`
B. `Delta l 5 mm` `Delta T 0.2 s` `n 20`
C. `Delta l 5 mm` `Delta T 0.1 s` `n 20`
D. `Delta l 1 mm` `Delta T 0.1 s` `n 50`

Answer

D

Explanation

(4) `g = (4 pi^(2) l)/(T^(2))`
`(Delta g)/(g) xx 100 = (Delta l)/(l) xx 100 + 2 (Delta T)/(T) xx 100`
`Delta l ` and `Delta T` are minimum for option `(d)` and also maximum number of observations are taken in option `(d)` only.