(a) Show that the gravitational field of a ring of uniform mass is zero at the center of the ring.

(b) Figure shows a point P in the plane of the ring but not at its center. Consider two elements of the ring of length s₁ and s₂ at distances of r₁ and r₂, respectively.

1. What is the ratio of the masses of these elements?

2. Which produces the greater gravitational field at point P?

3. What is the direction of the field at point P due to these elements?

(c) What is the direction of the gravitational field at point P due to the entire ring?

(d) Suppose that the gravitational field varied as 1/r rather than 1/r². What would be the net gravitational field at point P due to the two elements?

(e) How would your answers to parts (b) and (c) differ if point P were inside a spherical shell of uniform mass rather than inside a plane circular ring?

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