Question

A force 'F' is applied on a square plate of side 'L'. If the percentage error in determining 'L' is 3% and that in 'F' is 2% then the percentage error in determining the pressure is

• A. \(5\%\)
• B. \(6\%\)
• C. \(7\%\)
• D. \(8\%\)

Hint:

Density is mass divided by volume pi r squared l, so add relative errors with the radius error doubled.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The wire is a cylinder, so volume is \(\pi r^2 l\) and density is \(\rho = \frac{m}{\pi r^2 l}\).

Step 2: Key Formula or Approach:
\[ \frac{\Delta\rho}{\rho} = \frac{\Delta m}{m} + 2\frac{\Delta r}{r} + \frac{\Delta l}{l} \]

Step 3: Calculation:
\(\frac{\Delta m}{m} = \frac{0.003}{0.3} = 1\%\), \(\frac{\Delta r}{r} = \frac{0.005}{0.5} = 1\%\), \(\frac{\Delta l}{l} = \frac{0.06}{6} = 1\%\).
\[ \frac{\Delta\rho}{\rho}\times100 = 1 + 2(1) + 1 = 4\% \]
The error in radius counts twice, because r appears squared.

Final Answer:
The maximum error in density is 4 percent, option (A). \[ \boxed{4\%} \]