Physics And Measurement Question 291

Question: In a simple pendulum experiment, the maximum percentage error in the measurement of length is 2% and that in the observation of the time- period is 3%. Then the maximum percentage error in determination of the acceleration due to gravity g is

Options:

A) 5%

B) 6%

C) 1%

D) 8%

Show Answer

Answer:

Correct Answer: D

Solution:

[d] As we know, time period of a simple pendulum

$ T=2\pi \sqrt{\frac{L}{g}\Rightarrow g=\frac{4{{\pi }^{2}}L}{T^{2}}} $

The maximum percentage error in g $ \frac{\Delta g}{g}\times 100=\frac{\Delta L}{L}\times 100+2( \frac{\Delta T}{T}\times 100 ) $

$ =2$%$+2(3$%$)=8$%



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