Angle of repose and angle of friction are equal.

A block of mass $m$ slides along a floor while a force of magnitude $F$ is applied to it at an angle $\theta$ as shown in figure. The coefficient of kinetic friction is ${\mu }_K$. Then, the block's acceleration $a$ is given by : ($g$ is acceleration due to gravity)

The coefficient of static friction between two blocks is $0.5$ and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _______$\mathrm{N}$ (take $\left.g=10{ \mathrm{m} \mathrm{s}}^{-2}\right)$

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 $0.4$ ]