Spherical Shell - Variable Mass Density

A hollow spherical shell of radius 1 1 has its center at the origin of the x y z xyz coordinate system. The shell's variable area mass density is expressed as z 2 z^2 .

A test mass is positioned at ( x , y , z ) = ( 0 , 0 , 2 ) (x,y,z) = (0,0,2) . For simplicity, assume that the universal gravitational constant and test mass are both numerically equal to 1 1 .

What is the magnitude of the gravitational force exerted by the shell on the test mass?


The answer is 1.361.

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