JEE Mains · Physics · STD 11 - 3.2 motion in plane
The percentage error in the calculated volume of a sphere, if there is \(2\%\) error in its diameter measurement, is __________.
- A \(1\)
- B \(2\)
- C \(6\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
The volume of a sphere in terms of its diameter \(D\) is given by \(V = \dfrac{\pi}{6}D^3\) Taking the natural logarithm on both sides, we get \(\ln V = \ln\left(\dfrac{\pi}{6}\right) + 3 \ln D\) Differentiating for small errors, we obtain…
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