Well of death

The horizontal component of velocity of the particle remains constant throughout the course of motion since there is no acceleration in this direction. This component is $v_0\cos α=\dfrac{1}{\sqrt 2}$ . Here $v_0=1$ ms $^{-1}$ is the initial velocity of the particle and $α=45\degree$ is the angle of projection. Hence the force exerted by the particle on the wall of the cylinder is $\dfrac{mv_0^2}{R}\cos^2 α=\boxed {0.5}$ N ; $m=1$ kg. and $R=1$ m. are the mass of the particle and the radius of the cylinder respectively.