A physical quantity Q is calculated according to the expression Q is e...
Percentage Error in Q
To calculate the percentage error in a physical quantity Q, we need to consider the percentage errors in each of the variables involved in the expression for Q. In this case, the expression for Q is given as:
Q = a^3 * b^3 / (c√d)
Given that the percentage errors in A, B, C, and D are 2%, 1%, 3%, and 4% respectively, we can determine the percentage error in Q by considering each variable separately.
Percentage Error in a^3
The percentage error in a^3 can be calculated using the formula:
Percentage Error in a^3 = 3 * Percentage Error in a
Since the percentage error in A is 2%, the percentage error in a^3 would be:
Percentage Error in a^3 = 3 * 2% = 6%
Percentage Error in b^3
Similarly, the percentage error in b^3 can be calculated using the same formula:
Percentage Error in b^3 = 3 * Percentage Error in b
Given that the percentage error in B is 1%, the percentage error in b^3 would be:
Percentage Error in b^3 = 3 * 1% = 3%
Percentage Error in c√d
The percentage error in c√d can be calculated using the formula:
Percentage Error in c√d = 0.5 * Percentage Error in c + 0.5 * Percentage Error in d
Given that the percentage errors in C and D are 3% and 4% respectively, the percentage error in c√d would be:
Percentage Error in c√d = 0.5 * 3% + 0.5 * 4% = 1.5% + 2% = 3.5%
Percentage Error in Q
Finally, we can calculate the percentage error in Q by summing up the individual percentage errors in a^3, b^3, and c√d:
Percentage Error in Q = Percentage Error in a^3 + Percentage Error in b^3 + Percentage Error in c√d
Percentage Error in Q = 6% + 3% + 3.5% = 12.5%
Therefore, the percentage error in Q is 12.5%.
A physical quantity Q is calculated according to the expression Q is e...
Q=14%
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