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A sphere of radius R has its centre at t...

A sphere of radius `R` has its centre at the origin. It has a uniform mass density `rho_(0)` except that there is a spherical hole of radius `r=R//2` whose centre is at `x=R//2` as in fig (a) find gravitational field at points on the axis for `xgtR` (ii) Show that the gravitational field inside the hole is uniform, find its magnitude and direction.

Text Solution

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`vec(g) = + (pi G rho_(0) R^(3))/(6)[(1)/((x-(R )/(2))^(2))-(8)/(x^(2))], vec(g) = -(2pi Grho_(0)R)/(3) vec(i)`
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