3 A particle \(P\) of mass 3.5 kg is attached to one end of a light elastic string of natural length 0.8 m and modulus of elasticity 75 N . The other end of the string is attached to a fixed point \(O\). The particle rotates in a horizontal circle with a constant angular velocity of \(3 \mathrm { rad } \mathrm { s } ^ { - 1 }\). The centre of the circle is vertically below \(O\). The magnitude of the tension in the string is \(T \mathrm {~N}\) and the length of the extended string is \(L \mathrm {~m}\) (see diagram).
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1. By considering the acceleration of \(P\), show that \(T = 31.5 L\).
2. Write down another relationship between \(T\) and \(L\).
3. Find the value of \(T\) and the value of \(L\).
4. Find the angle that the string makes with the downwards vertical through \(O\).