An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha $ with the vertical, the maximum possible value of $\alpha $ so that the insect does not slip is given by

A horizontal force of $40\,N$ is applied to a $5\, kg$ block which is at rest on the horizontal surface. If the coefficient of kinetic friction is $0.4$, then the acceleration of the block is …….. $m/s^2$ $(g = 10 \,m/s^2)$

A block placed on a rough horizontal surface is pulled by a horizontal force $F$. Let $f$ be the force applied by the rough surface on the block. Plot a graph of $f$ versus $F$.

A sphere of mass $m$ is set in motion with initial velocity $v_o$ on a surface on which $kx^n$ is the frictional force with $k$ and $n$ as the constants and $x$ as the distance from the point of start. Find the distance in which sphere will stop