Question

In the given figure, a smooth parabolic wire track lies in the `xy`-plane (vertical). The shape of track is defined by the equation `y=x^(2)`. A ring of mass `m` which can slide freely on the wire track, is placed at the position `A (1,1)`. The track is rotated with constant angular speed `omega` such that there is no relative slipping between the ring and the track. The value of `omega` is

A. `sqrt(g//2)`
B. `sqrtg`
C. `sqrt(2g)`
D. `2sqrtg`

Answer 1

Correct Answer - C
`N cos theta=mg and N sin theta=momega^(2)r`
`:.tan theta=(omega^(2)r)/g`...(i)
Given `y=x^(2), :.(dy)/(dx)=2x`
or `tan theta =2xx1=2`..(ii)
From above equation, we get
`omega=sqrt(2g) (r=1m)`