A simple pendulum has a period of 5 77 seconds ... - JAMB Physics 2023 Question

The new length of the pendulum can be determined by setting up an equation based on the relationship between the period (\(T\)) and the length (\(L\)) of a simple pendulum. The formula \(T^2 \propto L\) is used, where \(T\) is the period.

Let the original length be \(L = x\) meters, and the new length be \(L - 3\) meters. The equation becomes:

\[
\frac{T_1^2}{L} = \frac{T_2^2}{L - 3}
\]

Substituting the given values:

\[
\frac{5.77^2}{x} = \frac{4.60^2}{x - 3}
\]

Solving for \(x\):

\[
33.29(x - 3) = 21.16x
\]

\[
33.29x - 99.87 = 21.16x
\]

\[
12.13x = 99.87
\]

\[
x = \frac{99.87}{12.13} \approx 8.23 \, \text{m}
\]

The new length of the pendulum is \(x - 3 \approx 5.23 \, \text{m}\).

Therefore, the correct option is: \(5.23 \, \text{m}\).