A block of mass m is projected on a smooth horizontal circular track with velocity v. What is the average normal force exerted by the circular walls on the block during its motion from A to B ?

\(\frac{2 mv^2}{\pi R}\)

Change in linear momentum of block : \(\Delta p\)

\(\Delta p = 2 mv\) 

Time taken to move from A to B : \(\Delta t\)

\(\Delta t = \frac{\pi R}{v}\)

Force exerted on the block = \(\frac{\Delta p}{\Delta t} = \frac{2 m v^2}{ \pi R}\)