The period of oscillation of simple pendulum is T = 2 π g L . Here L is about 10 cm and is known to 1 mm accuracy. The period of oscillation 0.5 sec. . The time of 100 oscillations is measured wit

Question

The period of oscillation of simple pendulum is T = 2 π g L ​ ​ . Here L is about 10 cm and is known to 1 mm accuracy. The period of oscillation 0.5 sec. . The time of 100 oscillations is measured with wristwatch of 1 sec . resolution. What is the accuracy in the determination of g

TestHub · Accepted Answer

The time period of a simple pendulum is

$T = 2 π \frac{L}{g} .$

Rewriting for g:

$g = \frac{4 π ^{2} L}{T ^{2}} .$

Using error propagation for products and powers:

$\frac{Δ g}{g} = \frac{Δ L}{L} + 2 \frac{Δ T}{T} .$

Given:

$\frac{Δ T}{T} \times 100% = 2%, \frac{Δ L}{L} \times 100% = 1%.$

Substitute into the error formula:

$\frac{Δ g}{g} \times 100% = 1% + 2 (2%) = 5%.$

Final Answer: The percentage error in the determination of g is 5%.

Physics - Error Question with Solution | TestHub

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