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In order to find the radius of gyration of a car, it is suspended with its axis vertical from three parallel wires 2.5 metres long. The wires are attached to the rim at points spaced 120° apart and at equal distances 250 mm from the axis. It is found that the wheel makes 50 torsional oscillations of small amplitude about its axis in 170 seconds. Find the radius of gyration of the wheel.

In order to find the radius of gyration of a car, it is suspended with its axis vertical from three parallel wires 2.5 metres long. The wires are attached to the rim at points spaced 120° apart and at equal distances 250 mm from the axis. It is found that the wheel makes 50 torsional oscillations of small amplitude about its axis in 170 seconds. Find the radius of gyration of the wheel. Correct Answer 268 mm

Given : l = 2.5 m ; r = 250 mm = 0.25 m ; Since the wheel makes 50 torsional oscillations in 170 seconds, therefore frequency of oscillation, n = 50/170 = 5/17 Hz Let kG = Radius of gyration of the wheel We know that frequency of oscillation (n), 5/17 = r/2πkG √g/l = 0.25/2πkG√9.81/2.5 = 0.079/kG kG = 0.079 x 17/5 = 0.268 m = 268 mm.

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