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Mechanical Properties Of Fluids

Question
CBSEENPH11020261

The period of oscillation of a simple pendulum is straight T space equals space 2 straight pi space square root of straight L over straight g end root . The measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is:

  • 2%

  • 3%

  • 1%

  • 5%

Solution

B.

3%

Time period,
straight T space equals space 2 straight pi space square root of straight L divided by straight g end root
thus, changes can be expressed as
plus-or-minus fraction numerator 2 increment straight T over denominator straight T end fraction space equals space plus-or-minus fraction numerator increment straight L over denominator straight L end fraction space plus-or-minus fraction numerator increment straight g over denominator straight g end fraction
According to the question, we can write
fraction numerator increment straight L over denominator straight L end fraction space equals space fraction numerator 0.1 over denominator 20.0 end fraction cm space equals space 1 over 200
Again time period
straight T space equals space 90 over 100 straight s
and space increment straight T space equals space 1 over 100 straight s
rightwards double arrow space fraction numerator increment straight T over denominator straight T end fraction space equals space 1 over 90
Now comma space
because space straight T space equals space 2 straight pi space square root of straight L over straight g end root
straight g space equals 4 straight pi squared straight L over straight T squared
fraction numerator increment straight g over denominator straight g end fraction space equals space fraction numerator increment straight L over denominator straight L end fraction space plus space fraction numerator 2 increment straight T over denominator straight T end fraction
or space fraction numerator increment straight g over denominator straight g end fraction straight x space 100 percent sign space equals space open parentheses fraction numerator increment straight L over denominator straight L end fraction close parentheses straight x 100 percent sign space plus space open parentheses fraction numerator 2 increment straight T over denominator straight T end fraction close parentheses straight x space 100 percent sign
space equals space open parentheses 1 over 200 straight x 100 close parentheses percent sign space plus space 2 space straight x space 1 over 90 space straight x space 100 percent sign
space equals space 2.72 percent sign space almost equal to space 3