question_answer

A small block is shot into each of the four tracks as shown below. Each of the frictionless track rises to the same height. The speed, with which the block enters the tracks, is same in all cases. At the highest point of the track, normal reaction is maximum in :

A)                                                

B)                

C)                                                               

D)

Correct Answer: A

Solution :

                 Since the block rises to the same heights in all thefour cases, from conservation of energy, speed ofthe block at highest point will be same in all fourcases. Say it is \[{{v}_{0}}.\]Equation of motion will be \[N+mg=\frac{mv_{0}^{2}}{R}\]                 or            \[N=\frac{mv_{0}^{2}}{R}-mg\] R (the radius of curvature) in first case isminimum. Therefore, normal reaction N willbe maximum in first case.