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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 from time of 100 oscillation with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy. The accuracy in the determination of g is found to be x%. The value of x is ______.

Asked in JEE Main 28th July 2nd Shift 2022 · Error and accuracy in g

Answer: 5

Step-by-step solution

Given: L=10 cm with Δ L=1 mm=0.1 cm; 100 oscillations timed with a 1 s watch.

Total time =100×0.5=50 s, so Δ t=1 s on 50 s.

g=(4π²L)/(T²), so (Δ g)/g=(Δ L)/L+2(Δ t)/t.

=(0.1)/(10)+2×1/(50)=0.01+0.04=0.05.

x=5.

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