A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downward as in figure and whose equation is\[{{x}^{2}}=ay\]. If the coefficient of friction is \[{{M}_{1}}\] the highest distance above the x-axis at which the particle will be in equilibrium is

• A. \[\mu a\]
• B. \[{{\mu }^{2}}a\]
• C. \[\frac{1}{4}{{\mu }^{2}}a\]
• D. \[\frac{1}{2}\mu a\]