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Q.

Student 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.

Student

Length of the pendulum (cm)

Number of oscillations (n)

Total time for ( ) oscillations (s)

Time period (s)

I

64.0

8

128.0

16.0

II

64.0

4

64.0

16.0

III

20.0

4

36.0

9.0

 

 

 

 

 

If  are the percentage errors in g, i.e  for students I, II and III respectively.

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a

  EIIis maximum

b

EI is minimum

c

EI=EII

d

EI=0

answer is B.

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Detailed Solution

Time period   T=2πlg

Or  tn=2πlg

%error in g=Δgg×100=(Δll+2Δtt)×100

EI=(0.164+2×0.1128)×100=0.3125%

EII=(0.164+2×0.164)×100=0.46875%

 EIII=(0.120+2×0.136)×100=1.055%

Here    EI  is minimum

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Student 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.StudentLength of the pendulum (cm)Number of oscillations (n)Total time for ( ) oscillations (s)Time period (s)I64.08128.016.0II64.0464.016.0III20.0436.09.0     If  are the percentage errors in g, i.e  for students I, II and III respectively.