Does a heavy body move with the slightest force on a frictionless surface? If I apply horizontal force on a body resting on the ground, my force will be opposed by the frictional force and the body will accelerate at the point where my force exceeds the force of friction = $\mu\, \mathrm{N}$ ($\mathrm{N}$ being the normal and $\mu$ being the coefficient of friction). In this case, the threshold value will be $\mu mg$ where $m$ is the mass of the resting body since $\mathrm{N} = mg$.
Is the following statement then true: Regardless of the mass/weight of the body, if the body is placed on a frictionless surface, the body will move with the slightest force? 
 A: When a force is applied to a body initially at rest for a finite amount of time, the velocity of that body is given by conservation of momentum:
$$m\Delta v = F\Delta t$$
When initial velocity is zero, $\Delta v = v$ - the final velocity is equal to the change in velocity. So we can write
$$v = \frac{F\Delta t}{m}$$
From this it can be seen that regardless of the size of $F$, $m$ and $\Delta t$, as long as all of them are finite, there will be a final velocity $v$.
Whether you can actually measure this velocity is a separate topic...
A: (Classical Physics only) 
Any massive body has a property known as inertia, thus even a body floating in outer space would require some kind of force to be accelerated. Using Newtons second law, you would find 
$$\tag{NII} \sum \vec{F} = \frac{\mathrm{d}}{\mathrm{d}t}\vec{p},$$ which for constant mass and one-dimensional motion simplifies to 
$$\tag{NII'} F = m a,$$ where $F$ is the force mentioned by the OP and $a$ is the acceleration of the center of mass of the body ($m$ is its mass). For example, suppose the body has a huge mass of $10^{10}$ kg and that you push it with a force of 1 N. This gentle (gentle is relative here of course) force would then give the body an acceleration of 
$$\frac{1}{10^{10}}\text{m/s^2} = 10^{-10}\text{m/s^2}. $$
Integrating this you would get the velocity (as a function of time) of the huge gigantic body to be 
$$v(t) = 10^{-10}\cdot t,$$ where $t$ is time (we've taken starting velocity to be $v(0) = 0$ m/s). 
Now according to this site a garden snail can move with a speed of 0.03mph or in m/s $$v_{snail} = 0.0134112 \mathrm{~m/s} $$ so in order for the huge body to move at the speed of a snail, you would have to put a constant force of 1 N for a time period given by 
$$T = \frac{0.0134112}{10^{-10}}\mathrm{~s} \approx 51 \text{months}. $$
As for the frictionless surface: since the force of gravity on earth would be perpendicular to the surface, the above analysis would apply in the horizontal direction (if the force of gravity would not be perp to the frictionless surface, well then the huge body would move due to the pull of gravity any way). 
A: Yes, indeed this is true.  We can suppose the contradictory case to prove the result.
Suppose on a frictionless surface we place a body and then push or pull it, amazingly it does not move. Now since we can observe only a single unbalanced force the body should have moved still it does not so we try to find that which force has been counteracting our force. After a tedious amount of searching here and there we still do not find any force, then surely the body must move and our assumption that it wont move is wrong, so lets try it practically to engrave our findings in stone. After spending a lot we make some superconductors and perform levitation for a sufficiently long rail, place a body to be levitated and then try pushing with the least force you can. Not only it always moves, it continues to move in absense of air resistance till the end of rail. Therefore yes any body on frictionless surface would move with slightest of push or pull.
