A person pushes a box on a rough horizontal platform surface. He… | JEE Main 2020 (4 Sep, Shift 2)

Q14JEE Main 2020 · 4 SEP · SHIFT 2Medium

Work by a Variable Force

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?

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Answer: (b)

Work = area under the $F$ - $x$ graph.
First 15 m (constant 200 N): $W_1 = 200 \times 15 = 3000\text{ J}$
Next 15 m (200 N falling linearly to 100 N, trapezium): $W_2 = \frac{1}{2}(200 + 100)(15) = 2250\text{ J}$
$W = 3000 + 2250 = 5250\text{ J}$ , so the answer is (b).

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