A wedge of mass $2m$ and a cube of mass $m$ are shown in figure. Between cube and wedge, there is no friction. The minimum coefficient of friction between wedge and ground, so that wedge does not move is

A block stays in equilibrium on an inclined plane. It is easiest to push along

A force $P=3mg$ acts on a block of mass $m$ at an angle of $30°$ with horizontal. The friction force between the block and ground (assuming $\mu =$ coefficient of friction between the contacting surface) is

A block is placed on a rough horizontal surface. The minimum force required to slide the block is

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 $g=10 \mathrm{m}/{\mathrm{s}}^2$ )