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A student performs an experiment for det...

A student performs an experiment for determination of `g = (4pi^(2) l)/(T^2)` and he commits an error of `Delta l `. For that he takes the time of n oscillations with the stop watch of least count `Delta T` and the commits a human error of 0.1 sec. For which of he following data, the measurement of g will be most accurate?

A

`{:(Deltal,DeltaT,n,"Amplitude of oscillation"),(5mm,0.2s,10,5mm):}`

B

`{:(Deltal,DeltaT,n,"Amplitude of oscillation"),(5mm,0.2s,20,5mm):}`

C

`{:(Deltal,DeltaT,n,"Amplitude of oscillation"),(5mm,0.1s,20,1mm):}`

D

`{:(Deltal,DeltaT,n,"Amplitude of oscillation"),(1mm,0.1s,50,1mm):}`

Text Solution

Verified by Experts

The correct Answer is:
D
The error in g is minimum when the number of oscillations i.e., n is more.
`(Deltag)/(g)=(Deltal)/(l)+|-2(DeltaT)/(T)|=(Deltal)/(l)+(2DeltaT)/(T)`
`(Deltal)/(l)+(2DeltaT)/(T)`, should be minimum.
Hence (d) represents the best measured data.
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