JEE Mains · Physics · STD 11 - Work,energy,power and collision
- JEE Mains 2020
- Hard
- Numerical
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 of \(100\, N\). 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\(........J\)\(?\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(5250\)
Step-by-step Solution
Detailed explanation
\(F =200 N \quad\) for \(0 \leq x \leq 15\)
\(=200-\frac{100}{15}( x -15)\) for \(15 \leq x <30\)
\(W =\int F dx\)
\(=\int_{0}^{15} 200 dx +\int_{15}^{30}\left(300-\frac{100}{15} x \right) dx\)
\(=200 \times 15+300 \times 15-\frac{100}{15} \times \frac{\left(30^{2}-15^{2}\right)}{2}\)
\(=3000+4500-2250\)
\(=5250 J\)
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