Question:
The length of rod is measured by meter scale having least count \(0.1\) cm and diameter is measured by vernier callipers having least count \(0.01\) cm. Length of rod is \(5.0\) cm and radius \(2.0\) cm. The percentage error in the calculated value of the volume is
The length of rod is measured by meter scale having least count \(0.1\) cm and diameter is measured by vernier callipers having least count \(0.01\) cm. Length of rod is \(5.0\) cm and radius \(2.0\) cm. The percentage error in the calculated value of the volume is
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Use dV/V = 2 dr/r + dL/L, with dr = 0.005 cm.
Updated On: Oct 1, 2026
- \(1\%\)
- \(2.5\%\)
- \(5\%\)
- \(7\%\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
Volume of a cylinder is \(V=\pi r^2L\). Percentage errors add up with multiplication by the power of each quantity.
Step 2: Error formula:
\[ \frac{\Delta V}{V}=2\frac{\Delta r}r+\frac{\Delta L}L \]
Step 3: Find the absolute errors:
The length has least count \(0.1\) cm, so \(\Delta L=0.1\) cm. The vernier measures the diameter with least count \(0.01\) cm, so \(\Delta d=0.01\) cm and hence \(\Delta r=0.005\) cm.
Step 4: Compute:
\(\dfrac{\Delta r}r=\dfrac{0.005}{2.0}=0.25\%\) and \(\dfrac{\Delta L}L=\dfrac{0.1}{5.0}=2\%\). So
\[ \frac{\Delta V}V\times100=2(0.25)+2=2.5\% \]
Step 5: Choose:
Option (B).
Final Answer:
The percentage error in volume is 2.5 percent. \[ \boxed{2.5\%} \]
Volume of a cylinder is \(V=\pi r^2L\). Percentage errors add up with multiplication by the power of each quantity.
Step 2: Error formula:
\[ \frac{\Delta V}{V}=2\frac{\Delta r}r+\frac{\Delta L}L \]
Step 3: Find the absolute errors:
The length has least count \(0.1\) cm, so \(\Delta L=0.1\) cm. The vernier measures the diameter with least count \(0.01\) cm, so \(\Delta d=0.01\) cm and hence \(\Delta r=0.005\) cm.
Step 4: Compute:
\(\dfrac{\Delta r}r=\dfrac{0.005}{2.0}=0.25\%\) and \(\dfrac{\Delta L}L=\dfrac{0.1}{5.0}=2\%\). So
\[ \frac{\Delta V}V\times100=2(0.25)+2=2.5\% \]
Step 5: Choose:
Option (B).
Final Answer:
The percentage error in volume is 2.5 percent. \[ \boxed{2.5\%} \]
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