51 A solid sphere of uniform density and mass M has radius 4 m Its...

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Physics

51 A solid sphere of uniform density and mass M has radius 4 m Its centre is at the origin of the coordinate system Two spheres of radii 1 m are taken out so that their centres are at P 0 2 0 and Q 0 2 0 respectively This leaves two spherical cavities What is the gravitational field at the origin of the coordinate axes 1 31GM 1024 3 31GM 52 In problem 51 what is the gravitational field at the centre of the cavities 31GM 1 1024 1 2 Gm 1024 4 Zero GM Gm 1024 3 31GM 53 In problem 51 what is the gravitational potential at any point on the circle x 6 2 2 4 GM GM 64 10 CH

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To solve these problems lets analyze each one step by step Problem 51 Gravitational field at the origin The original solid sphere has a uniform density rho and mass M with radius R 4 m The density is given by rho fracMfrac43 pi R3 Two smaller spheres of radius 1 m are removed each with a center at P0 2 0 and Q0 2 0 Mass of each removed sphere The volume of each smaller sphere is Vtextsmall frac43 pi 13 frac43 pi Therefore See Answer

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