A block rests on a rough inclined plane, making an angle $30°$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8.$ If the frictional force on the block is $10 \mathrm{N}$, the mass of the block (in $\mathrm{kg}$) is $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

In the arrangement shown in the figure, mass of blocks $B$ and $A$ is $2m$ and $m$, respectively. The surface between $B$ and the floor is smooth. The block $B$ is connected to block $C$ by means of a string pulley system. If the whole system is released, then find the minimum value of mass of block $C$, so that $A$ remains stationary with respect to $B$. The coefficient of friction between $A$ and $B$ is $\mu$.

A block $B$ is pushed momentarily along a horizontal surface with an initial velocity $v$. If $\mu$ is the coefficient of sliding friction between $B$ and the surface, then the block $B$ will come to rest after a time