Question

A particle moves along a curve y = x ^ 2 with constant speed of 10 m/s. When the particle is at origin, then the radius of curvature of path is n m. The value of n is

Answer 1

0.5

Answer 2

The radius of curvature for a curve y = f(x) is given by $\rho = \frac{[1 + (dy/dx)^2]^{3/2}}{|d^2y/dx^2|}$. For y = x^2, dy/dx = 2x and d^2y/dx^2 = 2. At the origin (x=0), dy/dx = 0 and d^2y/dx^2 = 2. Substituting these into the formula gives $\rho = \frac{[1 + 0^2]^{3/2}}{|2|} = \frac{1}{2} = 0.5$ m. Thus, n = 0.5.