$A$ $10\, kg$ block is placed on a horizontal surface as shown. If an external horizontal force $F = 50\, N$ is applied,find the friction force acting on the block. (Take $g = 10\, m/s^2$)

$A$ body of mass $m$ rests on a horizontal surface. The coefficient of friction between the body and the surface is $\mu$. If the mass is pulled by a force $P$ at an angle of $30^{\circ}$ with the horizontal as shown in the figure,the limiting friction between the body and the surface will be:

$A$ person is using scissors to cut a wire of circular cross-section and negligible weight. The wire slides in the direction away from the hinge until the angle between the scissors blades becomes $2 \alpha$. The friction coefficient between the blades and the wire is:

Find the minimum value of mass $m$ that should be placed on the $20 \, kg$ block so that the system remains at rest. (Given coefficient of friction $\mu = 0.25$) (in $, kg$)

If a pushing force making an angle $\alpha$ with the horizontal is applied on a block of mass $m$ placed on a horizontal table and the angle of friction is $\beta$,then the minimum magnitude of the force required to move the block is

Two masses $A$ and $B$ of $10\, kg$ and $5\, kg$ respectively are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown. The coefficient of static friction of $A$ with the table is $0.2$. The minimum mass of $C$ that may be placed on $A$ to prevent it from moving is ........ $kg$.