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Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table. Least count for length =0.1 ~cm Least count for time =0.1 ~s If E_ I , E_ II and E_ III are the percentage errors in g , i.e., ( g g 100 ) for students I, II a

Options

  1. AE_ I =0
  2. BE_ I is minimum
  3. CE_ I =E_ II
  4. DE_ II is maximum

Correct answer

B. E_ I is minimum

Step-by-step solution

aligned & T & =2 l g or t n =2 l g & g & = (4 ^2 ) (n^2 ) l t^2 aligned % error in g= g g 100= ( l l + 2 t t ) 100 aligned & E_ I = ( 0.1 64 + 2 0.1 128 ) 100=0.3125 % & E_ II = ( 0.1 64 + 2 0.1 64 ) 100=0.46875 % E_ III = ( 0.1 20 + 2 0.1 36 ) 100=1.055 % aligned Hence, E_ I is minimum. correct option is (b).

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