A block of mass M on a horizontal smooth surface is pulled by a load of mass $M /2$ by means of a rope AB and string BC as shown in the figure. The length & mass of the rope AB are L and M/2 respectively. As the block is pulled from $AB = L$ to $AB = 0$ its acceleration changes from

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Start (AB = L): the whole rope lies on the table. Moving mass $= M + \frac{M}{2} + \frac{M}{2} = 2 M$ ; driving force $= \frac{M}{2} g$ . $a = \frac{g}{4}$ .

End (AB = 0): the whole rope hangs. Driving force $= (\frac{M}{2} + \frac{M}{2}) g = M g$ ; mass $= 2 M$ . $a = \frac{g}{2}$ .

So the acceleration changes from $\frac{g}{4}$ to $\frac{g}{2}$ .

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