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Question: Answered & Verified by Expert
A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights hsph and hcyl on the inline. The ratio hsphhcyl  is given by:
PhysicsRotational MotionJEE MainJEE Main 2019 (08 Apr Shift 2)
Options:
  • A 25
  • B 45
  • C 1415
  • D 1
Solution:
2894 Upvotes Verified Answer
The correct answer is: 1415
From conservation of mechanical energy,
For solid sphere: 12msphV2+12Isphω2=msphghsph
V22+V25=ghsph 
7V210=ghsph …(i)
For cylinder: 12mcylV2+12Icylω2=mcylghcyl
V22+V24=ghcyl
3V24=ghcyl …(ii)
From (i) and (ii) hsphhcyl=1415

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