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

The figure shows a block kept on a rough and fixed inclined plane. The maximum external force down the incline for which the block remains at rest is $1 \mathrm{N}$ while the maximum external force up the incline for which the block is at rest is $7 \mathrm{N}$. The coefficient of static friction$\mu$ is

A solid cube of mass $5 \mathrm{kg}$ is placed on a rough horizontal surface in $xy-$plane as shown. The friction coefficient between the surface and the cube is $0.4$. An external force $\overrightarrow{F}=6\hat{\mathrm{i}}+8\hat{\mathrm{j}}+20\hat{\mathrm{k}} \mathrm{N}$ is applied on the cube (use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

If the coefficient of friction between wedge $A$ and block $B$ is $\mathrm{\mu }$, the maximum horizontal acceleration of the wedge $A$ for which the block $B$ will remain at rest with respect to the wedge is

A block of mass$M=5 \mathrm{kg}$ is resting on a rough horizontal surface for which the coefficient of friction is $0.2$. When the force $F=40 \mathrm{N}$ is applied, the acceleration of the block will be