Question

A physical quantity \(C\) is related to four other quantities \(P\), \(Q\), \(R\) and \(S\) as \(C=\frac{PQ^{2}}{R^{3}\sqrt{S}}\). The percentage error in the measurement of \(P\), \(Q\), \(R\) and \(S\) are \(1\%\), \(2\%\), \(3\%\) and \(2\%\) respectively. The percentage error in the measurement of \(C\) will be

• A. \(18\%\)
• B. \(6\%\)
• C. \(9\%\)
• D. \(15\%\)

Hint:

For a product or quotient of powers, the percentage errors add up after multiplying each by its power.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For \(C=\dfrac{PQ^{2}}{R^{3}\sqrt{S}}\), the maximum percentage error is the sum of each error multiplied by the magnitude of its power.

Step 2: Write the error formula
\(\dfrac{\Delta C}{C}\times100=\dfrac{\Delta P}{P}\times100+2\dfrac{\Delta Q}{Q}\times100+3\dfrac{\Delta R}{R}\times100+\dfrac{1}{2}\dfrac{\Delta S}{S}\times100\).

Step 3: Calculation
\(=1+2(2)+3(3)+\dfrac{1}{2}(2)=1+4+9+1=15\%\).

Step 4: Compare the options
The value \(15\%\) is option (D).

Final Answer:
The percentage error in C is 15 percent. \[ \boxed{\text{(D) }15\%} \]