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A student measures the acceleration due to gravity ( g ) using a simple pendulum. The length of the pendulum is measured as 20.0 cm using a meter scale of least count 0.1 cm. The time for 10 oscillations is measured as 20.0 s using a stopwatch of least count 0.1 s. The maximum percentage error in the determination of g is

Options

  1. A1.0 %
  2. B0.6 %
  3. C1.5 %
  4. D0.5 %

Correct answer

C. 1.5 %

Step-by-step solution

The formula for acceleration due to gravity using a simple pendulum is g = 4 ^2 L T^2 . The fractional error in the time period T is equal to the fractional error in the total time t for N oscillations, i.e., T T = t t . The maximum percentage error in g is given by: g g 100 = ( L L + 2 t t ) 100 Given values: L = 20.0 cm, L = 0.1 cm t = 20.0 s, t = 0.1 s Calculating individual percentage errors: Percentage error in L = 0.1 20.0 100 = 0.5 % Percentage error in t = 0.1 20.0 100 = 0.5 % Maximum percentage error in g

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