5. The diagram shows a fairground ride that consists of a number of seats suspended by chains that swing out as the centre rotates.
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When the ride rotates at a constant angular speed of \(\omega = 1.4 \mathrm { rads } ^ { - 1 }\), the seats move in a horizontal circle with each chain making an angle \(\theta\) with the vertical. Each of the seats and the chains may be modelled as light. Assume that all chains have the same length and are inextensible.
When a man of mass 75 kg occupies a seat, the tension in the chain is \(490 \sqrt { 3 } \mathrm {~N}\).
- Show that \(\theta = 30 ^ { \circ }\).
- Calculate the length of each chain.