A uniform disk of mass $\text{2m}$ and radius $\text{R}$ is placed freely on a smooth surface as shown in the figure. A particle of mass $\text{m}$ is connected to the circumference of the disc with a massless string. Now an impulse $\text{J}$ is applied on the particle in the direction shown by the dotted line. What is the acceleration of center of mass of the disk just after application of impulse?

$\text{Details}$ 1) Neglect friction everywhere. 2) $\text{J}=10$, $\text{m}=\sqrt{10}$ and $\text{R}=0.25$. 3)Each of the given quantities are in $\text{S.I.}$ units. >At first glance, it seems to me a question that uses chaos theory. However, since this is in my worksheet of Classical Mechanics, it must be elementary. I, however, am stunned and do not have the slightest idea of approaching this problem.