A physical quantity `x` is calculated from the relation `x = ( a^(2) b^(3))/(c sqrt( d))`. If the percentage error in `a, b , c , and d are 2% , 1% , 3%, and 4%`, respectively , what is the percentage error in `x`?
Text Solution
AI Generated Solution
To find the percentage error in the physical quantity \( x \) calculated from the relation
\[
x = \frac{a^2 b^3}{c \sqrt{d}},
\]
we will use the formula for the propagation of errors. The percentage error in a product or quotient of quantities can be determined by summing the relative errors (percentage errors) of each quantity, weighted by their respective powers in the formula.
...
An experiment from X = (a^(1//2) b^(2))/( c^(3)) . If the percentage errors in a, b , and c are +- 1% , +- 3% , and +- 2% , respectively , then the percentage error in X can be
A physical quantity A is related to four observable a,b,c and d as follows, A=(a^2b^3)/(csqrtd) , the percentage errors of measurement is a,b,c and d,are 1% , 3% , 2% and 2% respectively. What is the percentage error in the quantity A?
A physical quantity A is related to four observable a,b,c and d as follows, A=(a^2b^3)/(dsqrtc) , the percentage errors of measurement is a,b,c and d,are 1% , 3% , 2% and 1% respectively. What is the percentage error in the quantity A?
A physical quantity X is give by the relation X = (2h^(3)I^(2))/(2sqrt(n)) The percentage error in the meansurement of k ,I,m and n are 1% ,2%, 3% and 4% respectively The value of X is uncertain by
If the percentage errors of A,B,and C are a, b, and c, respectively ,then the total percentage error in the product ABC is
A physical quantity P is related to four observably a,b,c and d as follows P=a^(3)b^(3)//c^(1//2) 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?
An experiment measured quantity a, b, c and then x is calculated from x = ab^(2)//c^(3) . If the percentage error in a, b, c are pm 1%, pm 3% and pm 2% respectively, the percentage error in x can be,
An experiment measures quantites a, b, c and X is calculated from the formula X = (ab^(2))/(c^(3)) If the percentage errors in a,b,c are +- 1%, +- 3%, +- 2% respectively, the perentage error in X can be
A physcial quantity X is related to four measurable quantites a, b, c and d as follows : X = a^2 b^3 c^(5//2) d^(-2) The percentage error in the measurement of a, b, c and d are 1% , 2%, 3% and 4%, respectively. What is the percentage error in quantity X ? if the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result ?
A physical quantity y is given by y=(P^2Q^(3//2))/(R^4S^(1//2)) The percentage error in P,Q ,R and S are 1%,2%, 4% and 2% respectively. Find the percentage error in y.
