Answer:
(a)
(b)
(c-i) in straight rightward direction.
(c-ii)
(c-iii) to the bottom of horizontal right.
(d-i) to the horizontal right.
(d-ii) horizontally left
(d-iii) moving vertically downward
Explanation:
Given:
mass of hoop,
diameter of hoop,
angular speed of hoop,
So, time taken for 1 revolution(2π radians) of the hoop:
(a)
The center will move linearly in the right direction.
circumference of the hoop:
<u>Now the speed of center:</u>
(b)
Moment of inertia for ring about central axis:
where 'r' is the radius of the hoop.
∴Kinetic energy
(c) (i)
The highest point on the hoop will have the maximum velocity.
Given by:
in straight rightward direction.
(c) (ii)
Lowest point n the hoop will seem stationary for an observer on the ground.
(c) (iii)
Velocity of the right-most point of the loop.
This velocity will have 2 components horizontal right and vertical down.
here: is the downward component.
to the bottom of horizontal right.
When the observer is moving in the same direction with velocity:
(d) i
Then,
to the horizontal right.
(d) ii
The bottom point of hoop will seem to move horizontally left with velocity:
horizontally left
(d) iii
Contrary to the case of stationary observer, this observer will see the extreme right point of the hoop moving vertically downward with a velocity: