Work Done By A Variable Force
A force acting on a trolley along a straight track varies with position as F equals 6x newtons, where x is in metres. What is the work done by this force as the trolley moves from x equals 0 to x equals 4 m?
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About This Question
- Subject
- physics
- Chapter
- work, energy and power
- Topic
- work done by a variable force
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
48 J
As discussed in NCERT Class 11, Chapter 6 (Work, Energy and Power), when a force varies with position, the work done is the integral of F with respect to displacement, W = integral of F dx. Here F = 6x, so W = integral from 0 to 4 of 6x dx = 6 × [x²/2] from 0 to 4 = 3 × (4² - 0²) = 3 × 16 = 48 J. Geometrically this equals the area under the force versus position graph, which is a triangle of base 4 and height 24, giving (1/2)(4)(24) = 48 J. The option 24 J takes only the peak force value times one. The option 96 J forgets the factor of one-half in integration. The option 12 J uses an incorrect coefficient. A cross-check using the graph area gives the same 48 J, confirming the integral result.
This hard difficulty physics question is from the chapter work, energy and power, covering the topic of work done by a variable force. It appeared in the 2025 exam.
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