1. Understand the situation

Two blocks $A$ and $B$, each of mass $M$, are connected by a massless spring. A force $F$ is applied on block $B$.

We are told that block $A$ starts moving away from block $B$ with acceleration $a$.

This means the spring is affecting block $A$ in such a way that $A$ has acceleration of magnitude $a$ away from $B$.

2. Force on block $A$

Since the only horizontal force on block $A$ is the spring force, let the spring force be $T$.

By Newton's second law for block $A$:

$T = Ma$

So the spring exerts force $Ma$ on block $A$.

3. Force on block $B$

On block $B$, two horizontal forces act:

• Applied force $F$ in the direction shown
• Spring force $T = Ma$ in the opposite direction

Hence net force on $B$ is:

$F - T = F - Ma$

4. Acceleration of block $B$

Using Newton's second law for block $B$:

$M a_B = F - Ma$

Therefore,

$a_B = \frac{F - Ma}{M}$

5. Match with options

$a_B = \frac{F - Ma}{M}$

This corresponds to Option D.