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
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{t}{L}\) = \(\sqrt{(\frac{4\pi^2}{g}})\)
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\(^2\)
Source: Myschool Past Questions Archive (Record #42078)