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Q1. What is the minimal mass of helium (density 0.18) needed to lift a balloon carrying two people in a basket, if the total mass of people, basket, and balloon (but not gas) is 320?
Q2. In Santa's workshop, a mass m is attached to the rectangular frame by 4 springs and is constrained to move in the horizontal plane. The springs are not stretched in their equilibrium position. As everyone knows, Santa's workshop is located at North Pole and Earth is rotating around its axis.
a) Write down the system of disparity equations for small oscillation of the mass in the x-y plane.
b) Introduce a variable s=x+iy and combine the two equations. Write down the general solution of resulting differential equation.
c) Can you guess what would be the motion of the mass?
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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