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Paltu Sen
if you want to push the bodies with a force you should replace the strings by some solid rod. in this case the three masses attached with the rods act as a rigid body as a whole. if you assume the rods are massless the acceleration of the whole rigid body is still a=F/(m1+m2+m3). the values of compressive forces in each of these rods are same as the values of tensions in the corresponding strings.