A smooth horizontal fixed pipe is bent in the form of a vertical circle of radius `20m` as shown in figure. A small glass ball is shown in horizontal portion of pipe at speed `30m//s` as shown from end `A`. `(` Take `g=10m//s^(2))`

Which of the following statement is `//` are correct `:`
`(i)` ball will not come out from eend `B`.
`(ii)` ball will come out from end `B`.
`(iii)` At point `D` speed of ball will be just more than zero.
`(iv)` At point `E` and `C` the ball will have same speed.

Options

A. only `(i)`
B. `(ii)` and `(iv)`
C. `(ii),(iii)` and `(iv)`
D. only `(ii)`

Answer

B

Explanation

In the given situation if the speed becomes zero at the highest point then also the particle can complete the circle as there is no chance for the particle to loose constact in this case.
`u_(m i n)=` minimum speed required to complete vertical circle
`=sqrt(4gR)=sqrt(4xx10xx20)=sqrt(800)m//s`
`30 m//s gt sqrt(800)`
so it can easily complete the vertical circel
Now, for point `C`
`k_(f)+p_(f)=p_(i)+k_(i)`
`(1)/(2) mv_(c)^(2)+mgh_(c)=0+(1)/(2) m (30)^(2)`
`v_(c)^(2)=(30)^(2)-2gh_(c)`
As `h_(c)=h_(E)=R,` heights of points `C & E` from reference so `V_(E)=V_(C)`