A solid, homogeneous sphere of mass M and radius R is rolling down a rough inclined plane inclined at an angle $\theta$. Which of the following statements is INCORRECT?

For a solid sphere rolling down a rough inclined plane of angle $\theta$, the primary forces acting on it are its weight $mg$, normal reaction $N$, and static friction $f$.

The torque about the instantaneous point of contact is entirely due to the weight of the sphere, as the normal reaction and friction pass directly through this point. This torque is $\tau = mgR\sin\theta$. Since the net torque about the point of contact is non-zero, the angular momentum about this point is not conserved. Thus, the first statement is true.

The net torque about the center of mass of the sphere is provided only by the frictional force, given by $\tau_{cm} = fR$. The net torque about the point of contact is $mgR\sin\theta$. There is no standard axis for which the net torque evaluates to $mgR\cos\theta$. Thus, the second statement is incorrect.

During pure rolling, the instantaneous point of contact is at rest relative to the inclined surface. Therefore, the work done by static friction is zero, and the total mechanical energy of the system is conserved. Thus, the third statement is true.

The equation of translational motion parallel to the inclined plane is governed by the net force along that axis, which is $mg\sin\theta - f = ma$. The fourth statement presents this correct equation of motion.

Therefore, the incorrectly matched statement is the second one.

Answer: The net torque acting on the sphere is $mgR\cos\theta$