In the setup shown, blocks of masses 3m and 2m are placed on frictionless horizontal ground and the free end P of the thread is being pulled by a constant force F. Find acceleration of the free end P.

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The thread and pulleys exert a net pull of $3 F$ on block 3m and $2 F$ on block 2m, in opposite directions.

$a_{3 m} = \frac{3 F}{3 m} = \frac{F}{m}$ (one way) and $a_{2 m} = \frac{2 F}{2 m} = \frac{F}{m}$ (the other way).

The blocks move apart: relative acceleration $\frac{2 F}{m}$ .

From the thread constraint, $a_{P, 2 m} = \frac{6 F}{m}$ .

$a_{P} = \frac{6 F}{m} - \frac{F}{m} = \frac{5 F}{m}$ . Answer: (D).

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