Fewpal
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The system of particles shown in fig, is initially at rest. Find the value of force F that should be applied so that the system acquires a velocity of 6m/sec after moving 5m.

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Given data, 

Initial velocity u = 0

Final velocity v = 6m/sec

Distance traveled s = 5m

For finding acceleration, using the relation, v2 = 42 + 2as

∴ a = 3.6 m/sec2 62 = 0 + 2a X 5 ... (i)

Apply the relation F = ma,

Let T = Tension in the string, same for both side

Using the relation F = ma, for block A

T – 100 = ma T – 100 = (100/9.81) X 3.6 ...(ii) 

Using the relation F = ma, for block B 

100 + F – T = ma 

100 + F – T = (100/9.81) X 3.6 ...(iii) 

Add equation (2) and (3), we get 

F = 2[(100/9.81) X 3.6] 

F = 73.5N.

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