__Question 2.13__:

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

P = a

^{3}b

^{2 }

**/**(√c )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 of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?

__Solution__:

P = a

^{3}b

^{2}

**/**(√c)d

∆P/P = 3(∆a/a) +2(∆b/b) + (1/2)(∆c/c) + (∆d/d)

**(**(∆P/P) X 100

**)**% =

**(**3(∆a/a) X 100 + 2(∆b/b) X 100 + (1/2)(∆c/c) X 100 + (∆d/d) X 100

**)**%

= 3 X 1 + 2 X 3 + (1/2) X 4 + 2

= 13%

Percentage error in

*P*= 13 %

Value of

*P*is given as 3.763.

By rounding off the given value to the first decimal place, we get

*P*= 3.8.

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