A particle slides down a frictionless paraboli `(y=x^(2))` track `(A-B-C)` starting from rest at point `A`.Point `B` is at the vertex of parabola and point `C` is at a height less than that of point `A`.After `C`,the particle moves freely in air as a projectile. If the particle reaches highest point at `P`,then

Options

A. `KE` at `P=KE` at `B`
B. height at `P`=height at `A`
C. total energy at `P`=total energy at `A`
D. time of travel from `A` to `B` =time of travel from `B` to `P`

Answer

C

Explanation

In this type of question, nature of track is very important of consider, as friction is not in this track, total energy of the particle will remain constant throughtout the journey.
`(KE)_(B)gt(KE)_(P)`
`(PE)Plt(PE)A`
As, `height of p lt Height of A`
Hence, `path length AB gt path length BP`
Hence,time of travel from A "to" B ne Time of travel from B "to" P.