Explanation:

The situation described in the question involves a sphere of mass M that is kept in equilibrium using several springs. One of these springs applies a force f on the sphere, and we need to determine the acceleration of the sphere immediately after this particular spring is cut.

Understanding the Equilibrium:

Before the spring is cut, the sphere is in equilibrium. This means that the net force acting on the sphere is zero, resulting in zero acceleration. The forces acting on the sphere include the gravitational force (mg) and the forces exerted by the springs.

Force exerted by the Spring:

When the spring is intact, it applies a force f on the sphere. According to Hooke's Law, this force is directly proportional to the displacement of the spring from its equilibrium position. The equation for this force can be written as:

F = -kx

where F is the force exerted by the spring, k is the spring constant, and x is the displacement of the spring.

Effect of Cutting the Spring:

When the spring is cut, the force it applies on the sphere is no longer present. This results in a change in the forces acting on the sphere, leading to a non-zero net force and acceleration.

Determining the Acceleration:

To determine the acceleration of the sphere after the spring is cut, we need to consider the new forces acting on it. The only force remaining is the gravitational force (mg).

Since the net force is given by the equation:

Fnet = ma

where Fnet is the net force, m is the mass of the sphere, and a is the acceleration, we can write:

ma = mg

Simplifying this equation, we find:

a = g

Therefore, the acceleration of the sphere immediately after the spring is cut is equal to the acceleration due to gravity (g).

Conclusion:

When the particular spring is cut, the sphere will experience an acceleration equal to the acceleration due to gravity. This occurs because the force previously exerted by the spring is no longer present, resulting in a non-zero net force and acceleration.

Diagram