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A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres of equal radii 1 unit, with their centres at A (-2,0,0) and B(2,0, 0) respectively, are taken out of the solid leaving behind spherical carvities as shown in the figure., Then

  1. the gravitational force due to this object at the   origin is zero 
  2. the gravitational force at the point B(2,0,0) is   zero 
  3. the gravitational potential is the same at all points   of the circle  z squared plus y squared equals 36
  4. the gravitational potential is same at all points of   the circle y squared plus z squared equals 4 

The correct answers are: the gravitational force due to this object at the   origin is zero, the gravitational potential is the same at all points   of the circle  z squared plus y squared equals 36, the gravitational potential is same at all points of   the circle y squared plus z squared equals 4


    Sol: The mass of the sphere with cavities is symmetrically situated with respect to the origin. The circle y squared plus z squared equals 36 has a radius of 6 units and all points on it are at a distance of 6 units from the centre of the sphere where the whole mass of the sphere is supposed to be concentrated. The circle is outside the sphere. Similar is the case with circley squared plus z squared equals 4 .

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