Units and Measurement

Question

A physical quantity P is related to four observables a, b, c and d as follows :

$straight P space equals space straight a cubed straight b squared space divided by space square root of straight c straight d$
The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value ofP calculated using the above relation turns out to be 3.763, to what value should you round off the result?

Solution

Given space comma space straight P space equals space fraction numerator straight a cubed straight b squared over denominator open parentheses square root of straight c space straight d close parentheses end fraction space Maximum space fractional space error space in space straight p space is space given space by comma space fraction numerator increment straight P over denominator straight P end fraction space equals plus-or-minus open square brackets 3 fraction numerator increment straight a over denominator straight a end fraction space plus 2 fraction numerator increment straight b over denominator straight b end fraction space plus 1 half fraction numerator increment straight c over denominator straight c end fraction plus fraction numerator increment straight d over denominator straight d end fraction close square brackets space space space space space space space space space space space equals space plus-or-minus space open square brackets 3 1 over 100 space plus 2 3 over 100 space plus 1 half 4 over 100 plus 2 over 100 close square brackets space space space space space space space space space space equals space plus-or-minus space 13 over 100 space equals space plus-or-minus 0.13 space That space is comma space Percentage space error space in space straight P space equals space fraction numerator increment straight P over denominator straight P end fraction cross times 100 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals plus-or-minus 0.13 space cross times space 100 space equals plus-or-minus 13 space percent sign Value space of space straight P space equals space 3.763 On space rounding space off space the space given space value space to space the space first space place comma space straight P space equals space 3.8 space

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Units And Measurement

Some More Questions From Units and Measurement Chapter

What is the need of measurement?

Define physical quantity.

Give four examples of physical quantities.

Define unit.

What are the two main required characteristics of a unit?

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

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