A person pushes a box on a rough horizontal platform surface. He applies a force of $200 N$ over a distance of $15 m$ . Thereafter, he gets progressively tired, and his applied force reduces linearly with distance to $100 N$ . The total distance through which the box has been moved, is $30 m$ . What is the work done by the person, during the total movement of the box ?

3280 J

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2780 J

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5690 J

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5250 J

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Solution

The correct option is D $5250 J$
The given situation can be drawn graphically as shown in figure.

$Work done = Area under F-x graph$

$= Area of rectangle ABCD + Area of trapezium BCFE$

$W = (200 \times 15) + \frac{1}{2} (100 + 200) \times 15$

$= 3000 + 2250 = 5250 J$

Hence, $(D)$ is the correct answer.

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The correct option is D 5250 JThe given situation can be drawn graphically as shown in figure. Work done = Area under F-x graph = Area of rectangle ABCD + Area of trapezium BCFE W=(200×15)+12(100+200)×15 =3000+2250=5250 J Hence, (D) is the correct answer.