Question

Question #cfd30

Answer 1

The pendulum must be about `0.25 \text{m}` long (or `25 \text{cm}`).

Explanation:

The equation for the period of a pendulum is
`T \approx 2 \pi \sqrt{\frac{L}{g}}`
where `T` is the period, `L` is the length and `g` is acceleration due to gravity (`g \approx 9.81 \text{m/s}` on earth).

Solve for `L`:
`L \approx (\frac{T}{2 \pi})^2 g`

Substitute known values (in SI units):
`L \approx (\frac{1}{2 \pi})^2 9.81`
`L \approx 0.249 \text{m}`

As all other values used were in SI units, the answer is in SI units of length (meters).