Two masses $m$ and $2 m$ are connected by a string passing over a pulley fixed at the top of an inclined plane. The first mass moves vertically downwards drawing the second up the incline. If the angle of inclination is $\theta$ and the coefficient of friction is $\mu ,$ the acceleration of the system is less than it would be if the plane were smooth by an amount:

The system shown is just on the verge of slipping. The co-efficient of static friction between the block and the table top is

A block rests on a rough inclined plane making an angle of $30°$ 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 (take $g=10 \mathrm{m}/{\mathrm{s}}^2$ )

A $1 \mathrm{kg}$ block is being pushed against a wall by a force $F=75 \mathrm{N}$, as shown in the figure. The coefficient of friction is $0.25$. The magnitude of acceleration of the block is