A steel piano wire (Y = 2.0 1011 Pa) has a diameter of 0.80 mm. At

Question:

A steel piano wire (Y = 2.0 × 1011 Pa) has a diameter of 0.80 mm. At one end it is wrapped around a tuning pin of diameter 8.0 mm. The length of the wire (not including the wire wrapped around the tuning pin) is 66 cm. Initially, the tension in the wire is 381 N. To tune the wire, the tension must be increased to 402 N. Through what angle must the tuning pin be turned?