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A speedboat of mass 539 kg (including the driver) is tethered to a fixed buoy by a strong 33.3-m cable. The boat's owner loves high speed, but doesn't really want to go anywhere. So he revs up the boat's engine, makes a lot of noise, and runs the boat in circles around the buoy with the cable supplying all the necessary centripetal force. When the tension of the cable is steady at 1.29 × 104 N, with what force is the boat's engine pushing the boat? Different physics textbooks treat drag force somewhat differently and use different formulas. For the present purpose, take the water's drag force on the boat to be 450v2, where v denotes the boat's speed. Ignore any drag force on the cable.
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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