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The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N % . The value of N is:

Options

  1. A4
  2. B8
  3. C6
  4. D5

Correct answer

C. 6

Step-by-step solution

Time period of a simple pendulum is given by, T = 2 π l g . ⇒ g = 4 π 2 l T 2 Therefore, fractional error will be Δ g g = Δ l l + 2 Δ T T = 0 . 2 20 + 2 1 40 = 1 . 2 20 Percentage change = 1 . 2 20 × 100 = 6 %

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