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. (a)`mu a`
B. (b)`mu^(2) a`
C. (c)`(1)/(4) mu^(2) a`
D. (d)`(1)/(2) mu a`

Answer

C

Explanation

Sliding does not occur when `tan theta le mu`
`tan theta = (dy)/(dx) = (2x)/(a) = (2sqrt(ya))/(a) = 2 sqrt((y)/(a))` `:. 2 sqrt((Y)/(a)) le nu` `y le (a mu^(2))/(4)`