The figure below shows three groups of identical boxes that are being pulled by

Question

The figure below shows three groups of identical boxes that are being pulled by ropes along frictionless surfaces, accelerating to the left. The pulling force applied to the leftmost rope is the same for each group. Rank the boxes on the basis of the magnitude of their accelerations.

Choose from the following:

a4 = a5 = a6 > a2 = a3 > a1

a1 = a2 = a4 > a3 = a5 > a6

a1 = a2 = a3 = a4 = a5 = a6

a1 = a6 > a3 = a5 > a2 = a4

a1 > a2 = a3 > a4 = a5 = a6

a4 = a5 = a6 > a2 = a3 > a1

a1 = a2 = a4 > a3 = a5 > a6

a1 = a2 = a3 = a4 = a5 = a6

a1 = a6 > a3 = a5 > a2 = a4

a1 > a2 = a3 > a4 = a5 = a6

Explanation / Answer

Let the pulling force be F newton.
Let the mass of block = m

For 1st Group  
F = m * a
a1 = F/m ----------------1

For 2nd Group -
F - T = ma
where T = m*a
F = ma + ma
F = 2ma
a23 = F/2m ------------2

For 3rd Group -
F-T = ma
where T = ma + T'
and T' = ma
Thus ,
F = ma + ma + ma
F = 3ma
a456 = F/3m

Clearly we can see -

a1 > a23 >a456
Therefore ,
Correct Option = a1 > a2 = a3 > a4 = a5 = a6

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