A person pushes a box on a rough horizontal platform surface. He applies a force of $200 \mathrm{~N}$ over a distance of $15 \mathrm{~m}$. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to $100 \mathrm{~N}$. The total distance through which the box has been moved is $30 \mathrm{~m}$. What is the work done by the person during the total movement of the hox?
Correct Option: , 4
(4) The given situation can be drawn graphically as shown in figure.
Work done $=$ Area under $F-x$ graph
$=$ Area of rectangle $A B C D+$ Area of trapezium $B C F E$
$W=(200 \times 15)+\frac{1}{2}(100+200) \times 15=3000+2250$
$\Rightarrow W=5250 \mathrm{~J}$
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