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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

हिन्दी

In the system shown below, a light cord is wrapped around the rim of a uniform flywheel of mass \( M = 20 \text{ kg} \) and radius \( R = 20 \text{ cm} \) (mounted on a frictionless horizontal axle). A steady force \( F = 25 \text{ N} \) pulls the cord vertically downwards. If the cord unwinds for a duration such that the wheel makes \( 5 \) complete revolutions from rest, the work done by the pull is:

  1. \( 50\pi \text{ J} \)
  2. \( 100\pi \text{ J} \)
  3. \( 25\pi \text{ J} \)
  4. \( 200\pi \text{ J} \)

Correct answer · Option 1

\( 50\pi \text{ J} \)

Explanation

Length of cord unwound in 5 revolutions \( s = 5 \times (2\pi R) = 5 \times 2\pi(0.20) = 2\pi \text{ m} \). Work done \( W = F \times s = 25 \times 2\pi = 50\pi \text{ J} \).
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