# Circular Motion Question.

#### CosmicC

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

#### HallsofIvy

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.

#### CosmicC

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

PHF Hall of Fame
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.