Consider the ratioto be determined by measuring a dimensionless quantity a. If the error in the measurement of a is,then what is the error andDelta;r in determining r ?a)b)c)d)Correct answer is option 'B'. Can you explain this answer?

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Consider the ratio

to be determined by measuring a dimensionless quantity a. If the error in the measurement of a is

, then what is the error Δr in determining r ?

Correct answer is option 'B'. Can you explain this answer?

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PARAGRAPH “A”If the measurement errors in all the independent quantities are known, then it is possible to determine the error in any dependent quantity. This is done by the use of series expansion and truncating the expansion at the first power of the error. For example, consider the relation z = x/y. If the errors in x, y and z are Δx, Δy and Δz, respectively, then.The series expansion forto first power inΔy/yisThe relative errors in independent variables are always added. So the error in z will beThe above derivation makes the assumption thatΔx/x << 1,Δy/y<< 1,Therefore, the higher powers of these quantities areneglected.Q.Consider the ratioto be determined by measuring adimensionless quantity a.If the error in the measurement of a isthen what is the error Δrin determining r?

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Consider the following statements for dynamic characteristics of a measurement system: Fidelity is defined as the degree to which a measurement system indicates changes in the measured quantity without any dynamic error. Dynamic error is the difference between the true value of the quantity changing with time and the value indicated by the measurement system if no static error is assumed. Measuring lag is the retardation in the response of a measurement system to changes in the measured quantity.Which of the above statements are correct?

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The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5 % and 1 % the maximum error in determining the density is (

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In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion is 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 0.52s, 0.56s,0.57s, 0.54s and 0.59s. The least count of the watch used for the measurement of time period is 0.01s. Which of the following statement(s) is (ar e) true?

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In an experiment to determine the acceleration due to gravity g, the formula used for the time period of a periodic motion isThe 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 0.59s. The least count of the watch used for the measurement of time period is 0.01 s. Which of the following statement(s) is(ar e) true?

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Consider the ratioto be determined by measuring a dimensionless quantity a. If the error in the measurement of a is,then what is the error Δr in determining r ?a)b)c)d)Correct answer is option 'B'. Can you explain this answer?

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