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

As the given track `y=x^(2)` is a frictionless track thus, total energy (KE + PE) will be same throughout the journey.
Hence, total energy at A = Total energy at P. At B, the particle is having only KE but at P some KE is converted to P.
Hence, `" "` `(KE)_(B) gt (KE)_(P)`
Total energy at A = PE = Total energy at B =KE
Total energy at P
PE + KE
The potential energy at A, is converted to KE and PE at P, hence
`(PE)P lt (PE) A`
Hence, `" " ` (Height)P `lt` (Height)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.