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A shaft 1.6 m long is 95 mm in diameter for the first 0.6 m of its length, 60 mm in diameter for the next 0.5 m of the length and 50 mm in diameter for the remaining length. The shaft carries two rotors at two ends, the first having a mass of 800 kg and 0.85 m radius of gyration located at the 95 mm diameter end and the second having a mass of 600 kg and 0.55 m radius of gyration located at the other end. Determine the location of the node and natural frequency of torsional vibration of the system. Take C = 80GN/m2.
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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