Gravitational field due to spherical shell A point mass m is a distance d from the center of a thin spherical shell of mass M and radius R. The magnitude of the gravitational force on the point mass is given by the
where G is the gravitational constant.
a. Use the change of variable x = cos φ to evaluate the integral and show that if d > R, then
b. Show that if d < R (the point mass is inside the shell), then F = 0.
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Calculus: Early Transcendentals (3rd Edition)
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- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage