Four similar boxes are labelled I, II, III, and IV. The masses of I and III are equal and the masses of II and IV are equal. The mass of box I is smaller than that of box II. Boxes I and II are placed in a grass field and boxes III and IV are placed on a marble floor. Which box requires the maximum force to be moved?

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III

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Solution

The correct option is B II

Let us consider masses of boxes I, II, III and IV as $m_{1}$ , $m_{2}$ , $m_{3}$ , and $m_{4}$ respectively.

It is given that, $m_{1}$ = $m_{3}$ , $m_{2}$ = $m_{4}$ and $m_{1}$ < $m_{2}$ .
Thus, we can say that, $m_{3}$ < $m_{4}$ .

Frictional force is greater for heavier objects and smaller for lighter objects. Therefore, friction on box I < box II and friction on box III < box IV. Now we can say that, the maximum force required to move the box is either of box II or box IV.

Also, we know that irregular surfaces like grass fields offer more frictional force than smooth surfaces like marble floors. Therefore, frictional force on box II > box IV. Hence, box II requires the maximum force to move.

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