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You are to design a balloon capable of lifting 200 kilograms: the mass of the gas in the balloon must be 200 kilograms less than the mass of the ambient air it displaces. Pres-sure (ambient and in the balloon) is 100 kPa and ambient temperature is 300 K. Mass of the balloon fabric may be neglected. Determine the required balloon volume if
a) The balloon is filled with hot air at 400 K.
b) The balloon is filled with helium at ambient temperature.
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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