If a sphere is given a constant force along centre of mass, placed on a frictionless floor it does not undergo rotational motion as net torque about centre is zero. But why did we notice net torque about centre only? There exists a uniform torque of the force about topmost point ,so it must rotate about topmost point with constant angular acceleration, but it undergoes translational motion only. WHY?
It depends upon the distribution of the force applied to the sphere. Center of mass is an average, or aggregate measurement of all forces. If a single, horizontal, pinpoint force applies at the exact equatorial line of the sphere in your system, there will be no differential force that would cause the sphere to rotate. But if the force is distributed anywhere across the surface of the sphere, and if that force is not evenly balanced across all radial lines, then the resulting imbalanced force will create a net torque.
There exists a uniform torque of the force about topmost point ,so it must rotate about topmost point with constant angular acceleration, but it undergoes translational motion only. WHY?
There is no torque about the topmost point or the lowest point for the simple reason there is NOTHING preventing these points from moving: there's no friction.
Imagine the ball to be lightly squashed by a topmost horizontal plane and that friction between that plane and the topmost point exist. Now you have torque, making the ball rotate clockwise.
But in the absence of friction, no torques can develop.