C

To analyze the forces acting on the metal sphere, we will use the concepts of tension, weight, and normal force.
1. The tension in the string (T) must balance the vertical component of the weight (W) and also provide a net torque affecting the balance of forces.
2. The normal force (N) acting on the sphere can be derived from the tension and the angle θ:
N = T * cos(θ)
By applying Pythagorean theorem and trigonometric identities, we deduce that:
T² = N² + W²
thus, relating normal force and weight in terms of angles and components.
Hence, for (iii) N = (N² + W²), option [C] is correct. Therefore, the correct matches are: (iii) matches with [C].
Therefore, C.