A student performs an experiment for determination of `g = (4pi^(2)l)/(T^(2)) l ~~ 1m` and the commits an error of ''Deltal' For `T` he takes the time of n osciilations with the stop watch of least count `Deltat` For which of the following data the measurement of g will be most accurate ?
(a) `DeltaL = 0.5 DeltaL = 0.1, n = 20`
(B) `DeltaL = 0.5 Deltat = 0.1, n = 50`
(C) `DeltaL = 0.5, Deltat = 0.02 n =20` (D) `DeltaL = 0.1 Deltat = 0.05 n =50` .

Explanation

Here `T = ("total time")/("total oscillation") = (t)/(n) so dT = (dt)/(n)`
`(Deltag)/(g) = (DeltaL)/(L) + 2 (DeltaT)/(T)`
`(Deltag)/(g) = 90.5)/(1) + 2 (0.1//20)/(T)` (B) `(Deltag)/(g) = (0.5)/(1) + 2 (0.1//50)/(T)`
(C) `(Deltag)/(g) = (0.5)/(1) + 2 (0.02//20)/(T)` (D) `(Deltag)/(g) = (0.1)/(1) + 2 (0.05//50)/(T)`
So % error i g will be minimum in option `D` .