A) \[{{a}_{1}}>{{a}_{2}}>{{a}_{3}}>{{a}_{4}}\]
B) \[{{a}_{1}}>{{a}_{4}}>{{a}_{2}}>{{a}_{3}}\]
C) \[{{a}_{3}}>{{a}_{2}}>{{a}_{4}}>{{a}_{1}}\]
D) \[{{a}_{4}}>{{a}_{3}}>{{a}_{2}}>{{a}_{1}}\]
Correct Answer: B
Solution :
The motion of the boxes on the ground is opposed by the friction offered by the irregularities present on the surface. The magnitude of friction depends on the mass of the moving object. The greater the mass of the moving object, the more is the friction and vice-versa. Here all the boxes are cubical in shape and made up of the same material. Therefore, the friction of each box will depend on its volume, which is proportional to its mass. It is given that the distances are related as \[{{d}_{3}}>{{d}_{2}}>{{d}_{4}}>{{d}_{1}}.\] Hence, it can be inferred that the frictions offered by the ground to the boxes are related as: Friction on box 1 > Friction on box 4 > Friction on box 2 > Friction on box 3 Hence, the masses, i.e., the volumes in this case are related as: Mass of box 1 > Mass of box 4 > Mass of box 2 > Mass of box 3 Therefore, the sides of the boxes are related as: \[{{a}_{1}}>{{a}_{4}}>{{a}_{2}}>{{a}_{3}}\] The correct answer is B.
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