A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed towards downwards as in figure and whose equation is `x^2=ay`. If the coefficient of friction is `mu`, the highest distance above the x-axis at which the particle will be in equilibrium is

Options

A. `mua`
B. `mu ^(2) a `
C. `(1)/(4) mu ^(2) a `
D. `(1)/(2) mu a`

Answer

C

Explanation

For the sliding not to occur when
`tan theta = (dy)/(dx) = (2x)/(a) = mu implies x = ( mu a )/(2)`
`y = (x ^(2))/(a) = (( mu a )/(2)) ^(2) xx (1)/(a) = (1)/(4) mu ^(2) a `