Question

Mass and volume of a body are found to be \((6.00\pm 0.03)\) kg and \((2.00\pm 0.02)\) \(\text{m}^3\) respectively. Then the density of a body is

• A. \((3.00\pm 0.010)\) \(\text{kg/m}^3\)
• B. \((3.00\pm 0.015)\) \(\text{kg/m}^3\)
• C. \((3.00\pm 0.020)\) \(\text{kg/m}^3\)
• D. \((3.00\pm 0.045)\) \(\text{kg/m}^3\)

Hint:

For a quotient, the fractional errors add.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Density is \(\rho=m/V\). In a quotient the maximum fractional errors add up.

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

Step 3: Detailed Explanation
\(\rho=\dfrac{6.00}{2.00}=3.00\) kg/m\(^3\).
\(\dfrac{\Delta m}{m}=\dfrac{0.03}{6.00}=0.005\) and \(\dfrac{\Delta V}{V}=\dfrac{0.02}{2.00}=0.01\).
\[ \frac{\Delta\rho}{\rho}=0.015 \Rightarrow \Delta\rho=3.00\times0.015=0.045 \]
So \(\rho=(3.00\pm0.045)\) kg/m\(^3\).

Final Answer:
The density is \((3.00\pm0.045)\) kg/m\(^3\), option (D). \[ \boxed{(3.00\pm0.045)\ \text{kg/m}^3\ \text{(D)}} \]