In this problem, we are given a sphere of mass m that is kept in equilibrium using several springs. We need to determine the acceleration of the sphere immediately after one of the springs is cut.


To solve this problem, we need to consider the forces acting on the sphere both before and after the spring is cut.


Before the spring is cut, the sphere is in equilibrium, which means that the net force acting on it is zero.
- The weight of the sphere acts downwards with a force of mg.
- The springs apply an upward force on the sphere. Let's assume the force applied by the spring in question is f, and the total force applied by all the other springs is F.
- The normal force exerted by the ground on the sphere is also equal to mg, but in the opposite direction.


After the spring is cut, the force applied by that spring is no longer present. This changes the net force acting on the sphere and causes it to accelerate.
- The weight of the sphere remains the same, acting downwards with a force of mg.
- The total force applied by all the other springs remains the same, acting upwards with a force of F.
- The normal force exerted by the ground on the sphere also remains the same, equal to mg in the opposite direction.


To calculate the acceleration of the sphere, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
- Before the spring is cut, the net force is zero. So, we have:
0 = F - mg
F = mg
- After the spring is cut, the net force is equal to the difference between the upward force applied by the remaining springs and the weight of the sphere. So, we have:
ma = F - mg
ma = mg - mg
ma = 0
a = 0


After the particular spring is cut, the sphere will not move. The acceleration of the sphere is zero because the net force acting on it becomes zero.