Conservation Of Mechanical Energy
A child on a frictionless slide starts from rest at the top of a curved slide of vertical height 5 m. Taking g as 10 m/s squared, what is the speed of the child at the bottom of the slide?
Select the correct option:
Solution
10m/s
Following NCERT Class 11, Chapter 6 (Work, Energy and Power), when only gravity does work the total mechanical energy is conserved, so the loss in potential energy equals the gain in kinetic energy. Setting mgh = (1/2)mv², the mass cancels and v = sqrt(2gh). Substituting, v = sqrt(2 × 10 × 5) = sqrt(100) = 10 m/s. The curved shape of the slide does not matter because the normal force is always perpendicular to motion and does no work, and friction is absent. The option 5 m/s ignores the factor of 2 inside the root. The option 50 m/s forgets to take the square root. The option 7.1 m/s wrongly uses height alone without doubling. A sanity check: the result is independent of mass and of the path shape, depending only on the vertical drop, exactly as energy conservation predicts.
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About This Question
- Subject
- physics
- Chapter
- work, energy and power
- Topic
- conservation of mechanical energy
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
10m/s
Following NCERT Class 11, Chapter 6 (Work, Energy and Power), when only gravity does work the total mechanical energy is conserved, so the loss in potential energy equals the gain in kinetic energy. Setting mgh = (1/2)mv², the mass cancels and v = sqrt(2gh). Substituting, v = sqrt(2 × 10 × 5) = sqrt(100) = 10 m/s. The curved shape of the slide does not matter because the normal force is always perpendicular to motion and does no work, and friction is absent. The option 5 m/s ignores the factor of 2 inside the root. The option 50 m/s forgets to take the square root. The option 7.1 m/s wrongly uses height alone without doubling. A sanity check: the result is independent of mass and of the path shape, depending only on the vertical drop, exactly as energy conservation predicts.
This easy difficulty physics question is from the chapter work, energy and power, covering the topic of conservation of mechanical energy. It appeared in the 2025 exam.
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