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| The
earth moves about the sun in an elliptical orbit. As the
earth moves closer to the sun, which of the following
best describes the earth-sun system’s moment of
inertia? a. it is zero b. it decreases c. it increases d. it remains constant e. none of the above choices are valid Moment of inertia I = Sqmi ri2 As the earth moves closer to the sun, r decreases, but, mass of the system is constant. Q. A sphere shell has inner radius R, outer radius R, and mass M, distributed uniformly throughout the shell. Find the magnitude of the gravitational force exerted on the shell by a point particle of mass m located at a distance d from the center, outside the inner radius and inside the outer radius.
Mass of the sphere = M Point P is at a distance of d from the center and there is a particle of mass m located there. The mass of the spherical shell that will cause force will be mass located between the spheres of radius d and radius R1. That is mass of volume 4/3pd3 - 4/3pR13 = 4/3p(d3 - R13) Mass is distributed uniformly in the shell. Thus density of the shell is M/[4/3p(R23 - R13)] Thus M' = M/[4/3p(R23 - R13)] x 4/3p(d3 - R13) = [(d3 - R13)M]/(R23 - R13) Thus force exerted on m is = G.m.M' / d2 or F = [Gm(d3 - R13)M] / [d2(R23 - R13)] |
