Work Done By A Constant Force
A gardener pushes a lawn roller with a force of 150 N directed at 60 degrees below the horizontal, moving it 8 m along level ground. How much work does the applied force do on the roller?
Select the correct option:
Solution
600 J
As stated in NCERT Class 11, Chapter 6 (Work, Energy and Power), the work done by a constant force is W = F·d·cos(theta), where theta is the angle between the force and the displacement. The roller moves horizontally, while the force acts at 60 degrees below the horizontal, so the angle between force and displacement is 60 degrees. Computing the horizontal component: F·cos(60) = 150 × 0.5 = 75 N. The work is then W = 75 × 8 = 600 J. The vertical component of the force does no work because there is no vertical displacement. The option 1200 J wrongly uses the full force without the cosine factor. The option 1039 J mistakenly uses sin(60) instead of cos(60). The option 300 J halves the displacement incorrectly. A quick sanity check: only the component of force along motion transfers energy, so the answer must be less than the maximum possible 150 × 8 = 1200 J, and 600 J is exactly half, consistent with cos(60) = 0.5.
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About This Question
- Subject
- physics
- Chapter
- work, energy and power
- Topic
- work done by a constant force
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
600 J
As stated in NCERT Class 11, Chapter 6 (Work, Energy and Power), the work done by a constant force is W = F·d·cos(theta), where theta is the angle between the force and the displacement. The roller moves horizontally, while the force acts at 60 degrees below the horizontal, so the angle between force and displacement is 60 degrees. Computing the horizontal component: F·cos(60) = 150 × 0.5 = 75 N. The work is then W = 75 × 8 = 600 J. The vertical component of the force does no work because there is no vertical displacement. The option 1200 J wrongly uses the full force without the cosine factor. The option 1039 J mistakenly uses sin(60) instead of cos(60). The option 300 J halves the displacement incorrectly. A quick sanity check: only the component of force along motion transfers energy, so the answer must be less than the maximum possible 150 × 8 = 1200 J, and 600 J is exactly half, consistent with cos(60) = 0.5.
This easy difficulty physics question is from the chapter work, energy and power, covering the topic of work done by a constant force. It appeared in the 2025 exam.
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