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AP EAMCET · Maths · Application of Derivatives

If \(\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{~L}}{8}}, g\) is a constant and the relative error in T is \(k\) times to the percentage error in L then \(\frac{1}{k}=\)

  1. A \(2\)
  2. B \(\frac{1}{200}\)
  3. C \(200\)
  4. D \(\frac{1}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(200\)

Step-by-step Solution

Detailed explanation

\(T=2 \pi \sqrt{\frac{L}{g}} \Rightarrow \frac{d T}{d L}=\frac{\pi}{\sqrt{L g}}\) Relation error in \(T=\frac{d T}{T}=\frac{\pi}{\sqrt{L g}} d L \times \sqrt{\frac{g}{L}} \times \frac{1}{2 \pi}\) \(\Rightarrow \frac{d T}{T}=\frac{d L}{2 L}\) ....(i) Also,…