Question

A particle slides down a frictionless parabolic (y = x²) track (A – B – C) starting from rest at point A (Figure). 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

विकल्प

• KE at P = KE at B

• height at P = height at A

• total energy at P = total energy at A

• time of travel from A to B = time of travel from B to P

Answer 1

Total energy at P = total energy at A

Explanation:

As the given track y = x² is a frictionless track thus, the total energy (KE + PE) will be the 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 > (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 < (PE)A

Hence, (Height)P < (Height)A

As Height of P < Height of A

Hence, path length AB > path length BP

Hence, the time of travel from A to B ≠ Time of travel from B to P.