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Physics · UNITS AND MEASUREMENT

हिन्दी

In a simple pendulum experiment, the percentage errors in the measurement of length \( L \) and time period \( T \) are \( 2\% \) and \( 1.5\% \) respectively. The maximum percentage error in the estimated value of acceleration due to gravity \( g \) is:

  1. A
    \( 3.5\% \)
  2. B
    \( 5.0\% \)
  3. C
    \( 6.0\% \)
  4. D
    \( 1.0\% \)
View Answer & Solution

Correct answer · Option B

\( 5.0\% \)

Explanation

From \( T = 2\pi \sqrt{\frac{L}{g}} \implies g = 4\pi^2 \frac{L}{T^2} \). Max percentage error in \( g \) is \( \frac{\Delta g}{g}\% = \frac{\Delta L}{L}\% + 2\frac{\Delta T}{T}\% = 2\% + 2(1.5\%) = 5.0\% \).

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