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

(c): At B,m the velocity of verticle is more than the velocity at P .
Therefore K.E. at `ne` K.E. at Total energy is always conserved. i.e. . Total energy at (A.E=Total energy at B(K.E.))
=Total energy at P(P.E+K.E.)
Also as height of P `lt` height of A
`therefore` Path length AB `gt` path length BP
So, time of travel from A to B `ne` time of travel from B to P .
The correct option (c).