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^(2)a`

Answer

C

Explanation

For the sliding not to occur when
`tan theta le mu`
`tan theta=(dy)/(dx) =(2x)/a=(2sqrt(ay))/a=2sqrt(y/a)`
`:. 2sqrt(y/a) le mu` or `y le=(amu^(2))/4`