In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is T=2π7(R−r)5g . The values of R and r are measured to be (60±1) mm and (10±1) mm, respectively. In five successive measurements, the time period is found to be 0.52 s, 0.56 s, 0.57 s, 0.54 s and 0.59 s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(are) true?
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a
The error in the measurement of r is 10%
b
The error in the measurement of T is 3.57%
c
The error in the measurement of T is 2%
d
The error in the determined value of g is 11%
answer is Ü.
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Detailed Solution
Tmean=2.785Tmean=0.56% error in T =0.020.56×100=3.57%According to the question g∝T2R−r dgg=2dTT+dR+drR−rdgg=2(3.57%)+1+160−10×100% dgg×100=11% drr×100=110×100=10% Ans. (A, B, D)