Question

A bead is free to slide down a smooth wire tightly stretched between points `A` and `B` on a vertical circle. If the starts from rest at `A`, the heighest point on the circle

A. its velocity `v` on arriving at `b` is proportional to `cos theta`
B. its velocity `v` on arriving at `B` is proportional to `tan theta`
C. time to arrive at `B` is proportional to `cos theta`
D. time to arrive at `B` is independent of `theta`

Answer 1

Correct Answer - A::D
`AB = 2R cos theta`
(A) `v^(2) = u6(2) =2as`
`v^(2) = 2g cos theta xx 2R cos theta`
`v = 2 sqrt(Rg) cos theta`
`v prop cos theta`
(D) `S = ut +(1)/(2)at^(2)`
`2R cos theta = g cos thetat^(2)`
`t = sqrt((4R)/(g)) rArr t = 2 sqrt((R)/(g))`