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Question: Answered & Verified by Expert
A small disc of mass 500 gm and radius 5 cm rolls down an inclined plane without slipping. Speed of its center of mass when it reaches the bottom of the incline plane depends on
PhysicsGravitationTS EAMCETTS EAMCET 2021 (04 Aug Shift 1)
Options:
  • A mass & radius
  • B mass & height of the incline
  • C height of the incline
  • D height of the incline and acceleration due to gravity
Solution:
1158 Upvotes Verified Answer
The correct answer is: height of the incline and acceleration due to gravity

The loss in gravitational potential energy is equal to the gain in translational kinetic energy and rotational kinetic energy for the case of maximum velocity of sphere when it reaches ground. 

mgh=12Iω2+12mv2, here the relation, ω=vr and I=25mr2, it means, 

mgh=12×25mr2×vr22+12mv2=1225mv2+mv2gh=1275v2v=107gh

Only depends on height and acceleration due to gravity. 

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