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In the Jules Verne classic "A Journey to the Center of the Earth", Professor Hardwigg, his nephew Henry and Hans (the helper) travel down through a volcano towards the center of the Earth. Assuming their subterranean vehicle has a mass of 5 metric tons, what is the gravitational force exerted on the vehicle when they are at a distance of 572 km from the center of the Earth. Assume the Earth to be a uniform solid sphere. Take the Earth's mass to be 5.97*10^24 kg and the Earth's radius to be 6370 km. Take the positive radial direction to be outwards and express your answer in kilo-Newtons.
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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