Question

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 $\lambda$ (-2,0,0) and B (2,0,0) respectively, are taken out of the solid leaving behind spherical cavities as shown in figure. Then,

• A. the gravitational field due to this object at the origin is zero
• B. the gravitational field 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 1

Answer: (D)

the gravitational potential is the same at all points on the circle $y^2 + z^2 =4$

Answer 2

The gravitational field is zero at the centre of a solid sphere. The small spheres can be considered as negative mass m located at A and B. The gravitational field due to these masses at O is equal and opposite. Hence, the resultant field at O is zero (c and d ) $\rightarrow$ are correct because plane of these circles isy-z, i.e. perpendicular to x-axis i.e. potential at any point on these two circles will be equal due to the positive mass M and negative masses -m and -m.