Question

smooth cylindrical log of wood of radius R meter is fixed on a horizontal surface. the minimum speed with which a particle should be projected to reach the other side of the cylinder is ?

Answer 1

If the situation looks like this:

It is written that the log is smooth. In physics problems it means that there is no friction between the particle and the log. Also, it is written that the particle is fixed, according to the figure it means that the particle on the top is in unstable equilibrium. Thus, the particle needs any as low as possible or achievable speed to fall to the ground. The only thing the particle needs is some motion toward left or right to fall on the ground. The answer can be written as

$$v_{min}\ne0.$$