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A student uses a simple pendulum of exac...

A student uses a simple pendulum of exactly `1m` length to determine `g`, the acceleration due ti gravity. He uses a stop watch with the least count of `1sec` for this and record `40 seconds` for `20` oscillations for this observation, which of the following statement `(s) is (are)` true?

A

Error `DeltaT` in measuring T, the time period, is 0.05 second

B

Error `DeltaT` in measuring T, the time period, is 1 second.

C

Percentage error in the determination of g is 5%

D

Percentage error in the determination of g is 2.5%

Text Solution

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The correct Answer is:
A, C
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Three students S_1, S_2 and S_3 perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table. (Least count of length = 0.1 m least count for time = 0.1 s) If E_1, E_2 and E_3 are the percentage errors in 'g' for students 1, 2 and 3 respectively, then the minimum percentage error is obtained by student no._____.

Knowledge Check

  • A student uses a simple pendulum of exactly 1 m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 s for this and records 40 s for 20 oscillations. For this observation, which of the following statements is true?

    A
    Error `DeltaT` in measuring T, the time period, is 0.02 seconds.
    B
    Error `DeltaT` in measuring T, the time period, is 1 second
    C
    Percentage error in the deterinination of g is 5%.
    D
    Percentage error in the determination of g is 2.5%.

  • A student uses a simple pendulum of ecactly 1 m length to determine g, the acceleration due to gravity. He uses a stop watch with the least count of 1 s for this and records 40 s for 20 oscillation. For this observation, which of the following statement (s) is (are) true?

    A
    Error `DeltaT` in measuring T, the time period, is 0.05 s
    B
    Error `DeltaT` in measuring T, the time period is, 1 s
    C
    Percentage error in the determination of g is 5%
    D
    Percentage error in the determination of g is 2.5 %

  • Student I ,II , and III perform an experiment for measuring the acceleration due to gravity (g) usinf a simple pendulum. They use lengths of the pendulum and // or record time for different number of oscillations . The observations are shown in the following table . Least count for length = 0.1 cm {:(underset(III)underset(II)underset(I)underset()underset()("Student"),underset(20.0)underset(64.0)underset(64.0)underset((cm))underset("Pendulam")("Length of "),underset(4)underset(4)underset(8)underset((n))underset("n Oscillation")("Number of"),underset(9.0)underset(16.0)underset(16.0)underset((s))underset("Period")("Time")):} Least count for time = 0.1 s . If E_(I), E_(II) , and E_(III) are the percentage errors in g , i.,e., ((Delta g)/( g) xx 100) for students I,II , and III, respectively , then

    A
    `E_(I) = 0`
    B
    ` E_(I) is minimum`
    C
    `E_(I) = E_(II)`
    D
    `E_(II) is maximum`

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