A ring is released on a curve y=x^2, friction is sufficient such that ring rolls witout slipping. The value of force oof friction as a function of x is given by f=(Mgx/root(Nx^2+1)) , the value of N is:

Mass of ring : M Radius: R

Ans 4

At any given instant the rolling of the ring is equal to rolling on a rough inclined plane, which is tangential to given surface at that instant, at an angle given by

Formula for friction force of a rolling body without slipping on a rough inclined plane is given by , where K is the radius of gyration of the rolling body about an axis passing through its center of mass.

Given tan θ = 2x, then and K = 1 for a ring. Substituting these values we get .

Hence N = 4.