Circular Motion Question.

Aug 2017
2
0
A particle of mass m oscillates along arc AB on the inside of a smooth circular hoop of radius 'a' fixed in a vertical. The force on the hoop at any point is : ?
(a) k/a (b) k/3a (c) 2k/a (d) 3k/a
 
Aug 2010
434
174
The downward gravitational force on the object at any time is, of course, mg. The object does not go downward because the hoop is applying a force on it. That force is equal to the component of gravitational force perpendicular to the hoop. Let \(\displaystyle \theta\) be the angle the line from the center of the hoop makes with the vertical. The component of gravitational force perpendicular to the hoop is \(\displaystyle mg cos(\theta)\) and is also the force the object applies to the hoop. That does not appear to be any of the options you give. In particular, that force is not a constant- it is greatest at the bottom and least at the end points of the arc.
 
Aug 2017
2
0
Answer.

The downward gravitational force on the object at any time is, of course, mg. The object does not go downward because the hoop is applying a force on it. That force is equal to the component of gravitational force perpendicular to the hoop. Let \(\displaystyle \theta\) be the angle the line from the center of the hoop makes with the vertical. The component of gravitational force perpendicular to the hoop is \(\displaystyle mg cos(\theta)\) and is also the force the object applies to the hoop. That does not appear to be any of the options you give. In particular, that force is not a constant- it is greatest at the bottom and least at the end points of the arc.


I managed to solve it when i tried again. Check it out.
 

Pmb

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The downward gravitational force on the object at any time is, of course, mg. The object does not go downward because the hoop is applying a force on it. That force is equal to the component of gravitational force perpendicular to the hoop. Let \(\displaystyle \theta\) be the angle the line from the center of the hoop makes with the vertical. The component of gravitational force perpendicular to the hoop is \(\displaystyle mg cos(\theta)\) and is also the force the object applies to the hoop. That does not appear to be any of the options you give. In particular, that force is not a constant- it is greatest at the bottom and least at the end points of the arc.

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