$m_{1}$ and $m_{2}$ masses of two blocks are connected by a light spring on a smooth horizontal surface. The two masses are pulled apart and then released. Prove that the ratio of their acceleration is inversely proportional to their masses.

(N/A) According to Newton's third law of motion,the spring exerts equal and opposite forces on both masses.
Let $F_{1}$ be the force on mass $m_{1}$ and $F_{2}$ be the force on mass $m_{2}$.
Since the forces are equal in magnitude and opposite in direction,we have $F_{1} = -F_{2}$.
Using Newton's second law,$F = ma$,we can write:
$m_{1} a_{1} = -m_{2} a_{2}$
Here,$a_{1}$ and $a_{2}$ are the accelerations of the masses $m_{1}$ and $m_{2}$ respectively.
The negative sign indicates that the accelerations are in opposite directions.
Taking the magnitude of the ratio of accelerations:
$\frac{|a_{1}|}{|a_{2}|} = \frac{m_{2}}{m_{1}}$
This proves that the ratio of their accelerations is inversely proportional to their masses.