A, according to the balance of * * * point force, the spring force f = mg cos θ is obtained. At the moment of burning the rope, the spring had no time to deform and its elasticity remained unchanged. So, A is right and B is wrong.

C before burning, the tension of the rope t = mgtanθ. At the moment after burning, the elastic force remains unchanged, and the resultant force of elastic force and gravity is equivalent to the tension of the rope before burning, so at the moment after burning, the resultant force of the ball is mg tan θ, and according to Newton's second law, the acceleration a = gtan θ. So both c and d are wrong.

So choose a.