Let's assume the block is stationary only till point P . Slope of point P=tanθ (where, θ= angle of repose) also:
dy
dx
=
d
dx
(
x2
20
)=
x
10
⋅⋅⋅⋅⋅⋅⋅(i) We know that, the block will remain stationary only up till angle of repose. We know, angle of repose θ=tan−1(µs) ⇒θ=tan−1(0.5) ⇒tanθ=0.5⋅⋅⋅⋅⋅⋅⋅(ii) Now, equating (dy∕dx) at P.with tanθ from Eqs. (i) and (ii), we get