Question

A uniform sphere is placed on a smooth horizontal surface and a horizontal force F is applied on it at a distance h above the surface.The accerlation of the centre

Answer 1

Since the sphere is uniform the centre of mass is at the centre...also we know that for a body net external force= (total mass)*(acceleration of centre of mass) no matter where the force is applied...it just doesn't matter
Now the equation is as simple as F= Macm...where F is the net external force...the displacement time graph has a quadratic nature since the acceleration is constant...
Now if friction is present the whole picture changes...then the point of application becomes important(or so it seems)..as the friction depends on it(of course assuming pure rolling)...just write the translation component of newton's law for the spher i.e F-f=Macm....and then the write the rotational part F*x-f*R= I(alpha)...I is the moment of inertia about the central axis and R is taken as radius of the sphere...then apply (alpha)*R= acm...find the acceleration in terms of F,R and x and find the value of x for which the acceleration is maximum...