A wedge as shown in figure has a rough curved surface of coefficient of kinetic friction `(1)/sqrt(3)` whose shape can be given by equation `y=x^(2)`, where the horizontal direction is x-axis, vertical direction as y axis and the end of surface O as origin and x `&` y are measured in meter. A small block is released, from a certain point on the surface. The maximum height of the point from where block should be released so that it does not slip.

Options

A. `(1)/(4)m`
B. `(1)/(6)m`
C. `(1)/(12)m`
D. `(1)/(16)m`

Answer

C

Explanation

For no slipping `tantheta=mu=(dy)/(dx)=2x=(1)/sqrt(3)`
`rArrx=(1)/(2sqrt(3))rArry=x^(2)=(1)/(12)m`