A solid cylinder of mass $m$ is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is:

[The coefficient of static friction, ${\mu }_{\mathrm{s}}$, is $0.4$ ]

Consider the system shown below.

A horizontal force $F$ is applied to a block $X$ of mass $8 \mathrm{kg}$ such that the block $Y$ of mass $2 \mathrm{kg}$ adjacent to it does not slip downwards under gravity. There is no friction between the horizontal plane and the base of the block $X$. The coefficient of friction between the surfaces of the blocks $X$ and $Y$ is $0.5$. Take acceleration due to gravity to be $10 \mathrm{m} {\mathrm{s}}^{-2}$. The minimum value of $F$ is

Three blocks with masses $m$, $2m$ and $3m$ are connected by strings as shown in the figure. After an upward force $F$ is applied on block $m,$ the masses move upward at a constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)