To develop this problem it is necessary to apply the concepts related to a magnetic field in spheres.
By definition we know that the magnetic field in a sphere can be described as
Where,
a = Radius
z = Distance to the magnetic field
I = Current
Permeability constant in free space
Our values are given as
diameter of the sphere then,
Thus z = a
Re-arrange to find I,
Therefore the current at the pole of this sphere is 
Answer: momentum has the same direction as that of velocity but when 2 bodies with the same linear momentum & different velocities it has different masses because a vector quantity is represented by a cross product of mass and velocity of object .
Oh my gosh ! Resisting the force of gravity always DOES involve doing work.
If no work is being done, then you're NOT resisting the force of gravity.
Example:
-- ball rolling on the floor . . . no work
-- ball rolling up a ramp . . . work being done
-- ball rolling down a ramp . . . work being done, BY gravity
Explanation:
They probably put "rolls without slipping" in there to indicate that there is no loss in friction; or that the friction is constant throughout the movement of the disk. So it's more of a contingency part of the explanation of the problem.
(Remember how earlier on in Physics lessons, we see "ignore friction" written into problems; it just removes the "What about [ ]?" question for anyone who might ask.)
In this case, you can't ignore friction because the disk wouldn't roll without it.
As far as friction producing a torque... I would say that friction is a result of the torque in this case. And because the point of contact is, presumably, the ground, the friction is tangential to the disk. Meaning the friction is linear and has no angular component.
(You could probably argue that by Newton's 3rd Law there should be some opposing torque, but I think that's outside of the scope of this problem.)
Hopefully this helps clear up the misunderstanding for you.
