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If \(\frac{t}{L}\) = \(\sqrt{(\frac{4\pi^2}{g}})\), what is the value of g when L = 4.5; t =...

Mathematics
NECO 2002

If \(\frac{t}{L}\) = \(\sqrt{(\frac{4\pi^2}{g}})\), what is the value of g when L = 4.5; t = 5 secs

  • A. 3.20 ms2
  • B. 11.31 ms2
  • C. 32.00 ms2
  • D. 56.57 ms2
  • E. 160.00 ms2
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Correct Answer: Option C
Explanation

\(\frac{t}{L}\) = \(\sqrt{(\frac{4\pi^2}{g}})\)

Take square of both sides

\(\frac{t^2}{L^2}\) = \(\frac{4\pi^2}{g}\)

Cross multiply

t\(^2\)g = L\(^2\)4\(\pi\)\(^2\)

g = \(\frac{4\pi^2L^2}{t^2}\)

g = \(\frac{4 \times 4.5 \times 4.5  \pi^2}{5^2}\)

g = \(\frac{799.44}{25}\) = 31.9776 ≈ 32m/s\(^2\)


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