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In the movie Once Upon a Time in America, set in the Prohibition era, a clever ploy is used by bootleggers transporting liquor by boat. Attached to each case of liquor is a balloon of negligible weight and a cloth bag filled with salt as shown in the figure below. When police approach, the liquor is dumped overboard. Initially the cases sink, but after a time the salt dissolves and the balloons float to the surface. Suppose that a liquor case weighs 175 N and displaces 137 N of water and that, when the balloon floats, it is half submerged. Find the volume of the balloon and the required weight of salt.
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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