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1. John's mass is 93.4 kg, and Barbara's is 53.9 kg. He is standing on the x axis at xJ = +9.27 m, while she is standing on the x axis at xB = +4.16 m. They switch positions. How far and in which direction does their center of mass move as a result of the switch?
2. One object is at rest, and another is moving. The two collide in a one-dimensional, completely inelastic collision. In other words, they stick together after the collision and move off with a common velocity. Momentum is conserved. The speed of the object that is moving initially is 28 m/s. The masses of the two objects are 3.5 and 8.6 kg. Determine the final speed of the two-object system after the collision for the case (a) when the large-mass object is the one moving initially and the case (b) when the small-mass object is the one moving initially.
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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