[Physics] Can there be an acceleration when no net force acts on a massless object

forcesnewtonian-mechanics

If no net force acts on a massless object can there be any acceleration of the object?

My attempt:

$$F=ma\\ \implies a=F/m\\ \implies a=0/0 $$

$\implies a$ can be anything.

Best Answer

In a theory view point, it is possible. For example, consider figure below. The string is massless and inelastic (rigid). (There is no friction)

enter image description here

The string moves with the mass $m$, so its acceleration is $a=\large{\frac Fm}$. But, the net force acting on the string is zero.

enter image description here

$$\Sigma F_{\text{string}}=F-T=0$$