A physical quantity P is related to four observables a, b, c and d as follows : P = a³ 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 ?
Given, the percentage errors in the measurement of four observables a, b, c and d are 1%, 3%, 4% and 2% respectively and the calculated value of P is 3.763.
The relation between the P and four observables a, b, c and d is,
P = a 3 b 2 c d
Differentiate the above expression,
Δ P P = 3 Δ a a + 2 Δ b b + Δ c 2 c + Δ d d
Take the percentage in both side of the equation.
( Δ P P × 100 ) % = ( 3 Δ a a × 100 + 2 Δ b b × 100 + Δ c 2 c × 100 + Δ d d × 100 ) % = ( 3 × 1 + 2 × 3 + 1 2 × 4 + 2 ) = 13 %
Thus, the percentage error in quantity P is 13%.
The percentage error in the physical quantity P is,
( Δ P P × 100 ) % = 13 % Δ P = 13 P 100
Substitute the given value in the above expression.
Δ P = 13 × 3.763 100 = 0.48919
Since the error comes out up-to first decimal place, so the calculated value of P must be round off up-to first decimal place. Thus, calculated value of P after rounding off is 3.8.
Given, the percentage errors in the measurement of four observables a, b, c and d are 1%, 3%, 4% and 2% respectively and the calculated value of P is 3.763.
The relation between the P and four observables a, b, c and d is,
Differentiate the above expression,
Take the percentage in both side of the equation.
Thus, the percentage error in quantity P is 13%.
The percentage error in the physical quantity P is,
Substitute the given value in the above expression.
Since the error comes out up-to first decimal place, so the calculated value of P must be round off up-to first decimal place. Thus, calculated value of P after rounding off is 3.8.
