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A student performs an experiment for determination of $g [= \frac{4 π^{2} L}{T^{2}}], L \approx 1 m,$ and he commits an error of ΔL for T he takes the time of n oscillations with the stop watch of least count ΔT .For which of the following data the measurement of g will be most accurate?

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$ΔL = 0 .5, ΔT = 0 .1, n = 50$

$ΔL = 0 .5, ΔT = 0 .01, n = 20$

$ΔL = 0 .5, ΔT = 0 .1, n = 20$

$ΔL = 0 .5, ΔT = 0 .05, n = 50$

answer is D.

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Detailed Solution

$\frac{Δg}{g} = \frac{Δl}{l} + 2 \frac{ΔT}{T}$ ( Δl and ΔT are least, and the number of readings are maximum)

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