A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two sphere 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 cavities as shown if fig Then:

Options

A. The gravitational force due to this object at the origin is zero.
B. the gravitational force at the point B(2,0,0) is zero.
C. the gravitational potential is the same at all points of circle `y^2 +z^2 = 36`
D. the gravitational potential is the same at all points on the circle `y^2 +z^2 =4.`

Answer

A, C, D

Explanation

(a,c,d) The gravitational field intensity at the point O is zero
(as the cavities are symmetrical with respect to O.) Now the
force acting on a test mass `m_0` placed at O is given by
`F =m_0E = m_0xx0 = 0`
Now, `Y^2 +z^2 =36` represents the equation of a circle with
centre (0,0,0) and radius 6 units the plane of the circle is
perpendicular to x-axis.