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Q.

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured for time of 100 oscillation with a watch of 1 s resolution. If measured value of length is 10cm known to 1mm accuracy, the accuracy in the determination of g is found to be x %. The value of x is ……………

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answer is 5.

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Detailed Solution

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Time period of a simple pendulum, T=2πlg

Squaring on both sides

 T2=4π2lgg=4π2(lT2)Δgg=ΔII+2ΔTT

Percentage error in g is,
Δgg×100=Δll×100+2(ΔTT×100)=0.110×100+2×150×100=1%+4%=5%
 

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In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured for time of 100 oscillation with a watch of 1 s resolution. If measured value of length is 10cm known to 1mm accuracy, the accuracy in the determination of g is found to be x %. The value of x is ……………