Sol. The velocity of the body at B depends on how much of its potential energy the body will expend on work done against the force of friction. The forces of friction on routes 1 and 2 are not the same, since the pressures exerted by the body on the surface are not the same. This is conditioned by the following factors.

When moving along any curved path a body must have a centripetal acceleration. On route 1 this acceleration is directed downwards, on route 2 upwards.

This acceleration, whose direction is normal to the plane along which the body slides, arises because the component of the force of gravity which is normal to the surface and the normal reaction of the surface on the body are not equal in magnitude. The resultant of these two force (their difference) is what imparts to the body the necessary centripetal acceleration therefore on route 2 where the centripetal acceleration is directed upwards, the normal reaction is everywhere greater than the normal component of the force of gravity, and on route 1 it is less everywhere. The magnitude of the normal components of the force gravity are in general different for routes 1 and 2, since the angles between the normal to the plane and the vertical are different. But since both surfaces are of the same radius, the normal components of the force of gravity alter within the same limits on both routes, but in reverse order. Therefore we can say that the normal reaction of the surface on the body (and so of the body on the plane) is on average less on route 1 than on route 2. Since the coefficient of friction on both routes is the same, the force of friction is less on route 1 than on route 2, i.e. the work which is expended on overcoming the force of friction will be les on route 1. Thus at point B the body has greater kinetic energy, and so greater velocity, if it moves along route 1, not along route 2.