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Question

The percentage errors in the measurements of the length of a simple pendulum and its time period are 3% and 5% respectively. The maximum error in the value of the acceleration due to gravity obtained from these measurements is


A
2%
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B
8%
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C
13%
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D
15%
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Solution

The correct option is C 13%

T=2πlg or, g=4π2lT2or, log(g)=log(4π2) + log (l) 2log (T)
The maximum error in g, Δgg=Δll+2ΔTT=3% +(2×5%)=13%


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