A physical quantity 'x'is calculated from the relation x=a^3b^2/�ãcd. Calculate percentage error in x, if a, b, c and d are measured respectively with an error of 1%,3%,4% and 2%.
To calculate the percentage error in 'x', we will use the formula for percentage error:
Percentage Error = (Absolute Error / Measured Value) * 100
Let's calculate the percentage errors for each variable first.
For variable 'a', the percentage error is 1%:
Percentage Error in 'a' = (1 / a) * 100
For variable 'b', the percentage error is 3%:
Percentage Error in 'b' = (3 / b) * 100
For variable 'c', the percentage error is 4%:
Percentage Error in 'c' = (4 / c) * 100
For variable 'd', the percentage error is 2%:
Percentage Error in 'd' = (2 / d) * 100
Now, let's substitute the values in the given formula to calculate 'x':
x = (a^3 * b^2) / (c * d)
Now, we need to substitute the values of 'a', 'b', 'c', and 'd', along with their respective percentage errors, into the formula for 'x' to calculate the overall percentage error.
To calculate the overall percentage error, we will add up the individual percentage errors:
Overall Percentage Error = (Percentage Error in 'a' + Percentage Error in 'b' + Percentage Error in 'c' + Percentage Error in 'd')
Finally, substitute the percentage errors and calculate the overall percentage error in 'x'.