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A small connecting rod of mass 1.5 kg is suspended in a horizontal plane by two wires 1.25 m long. The wires are attached to the rod at points 120 mm on either side of the centre of gravity. If the rod makes 20 oscillations in 40 seconds, find the radius of gyration of the rod about a vertical axis through the centre of gravity.

A small connecting rod of mass 1.5 kg is suspended in a horizontal plane by two wires 1.25 m long. The wires are attached to the rod at points 120 mm on either side of the centre of gravity. If the rod makes 20 oscillations in 40 seconds, find the radius of gyration of the rod about a vertical axis through the centre of gravity. Correct Answer 107 mm

Given : m = 1.5 kg ; l = 1.25 m ; x = y = 120 mm = 0.12 m Since the rod makes 20 oscillations in 40 s, therefore frequency of oscillation, n = 20/40 = 0.5 Hz Let kG = Radius of gyration of the connecting rod. We know that frequency of oscillation (n), 0.5 = 1/2πkG √gxy/l = 1/2πkG √9.81 x 0.12 x 0.12/1.25 = 0.0535/k kG = 0.0535/0.5 = 0.107 m = 107 mm.

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