Question

A wire has mass \((0.2\pm0.002)\) gram, radius \((0.4\pm0.004)\) mm and length \((6\pm0.06)\) cm. The percentage error in the measurement of its density is

• A. 1 %
• B. 2 %
• C. 3 %
• D. 4 %

Hint:

Density is mass divided by volume; add the fractional errors with the right powers.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Density \(\rho=\dfrac{m}{\pi r^2 l}\), so \(\dfrac{\Delta\rho}{\rho}=\dfrac{\Delta m}{m}+2\dfrac{\Delta r}{r}+\dfrac{\Delta l}{l}\).

Step 2: Individual errors
\(\dfrac{\Delta m}{m}=\dfrac{0.002}{0.2}=1\%\), \(\dfrac{\Delta r}{r}=\dfrac{0.004}{0.4}=1\%\), \(\dfrac{\Delta l}{l}=\dfrac{0.06}{6}=1\%\).

Step 3: Calculation
Total \(=1+2(1)+1=4\%\).

Final Answer:
The percentage error in the density is 4 percent. \[ \boxed{\text{(D) }4\ \%} \]