A block of mass $5\,kg$ and surface area $2\,m ^2$ just begins to slide down an inclined plane when the angle of inclination is $30^{\circ}$. Keeping mass same, the surface area of the block is doubled. The angle at which this starts sliding down is :

A block of mass $M$ is held against a rough vertical well by pressing it with a finger. If the coefficient of friction between the block and the wall is $\mu $ and acceleration due to gravity is $g$, calculate the minimum force required to be applied by the finger to hold the block against the wall.

Why coefficient friction is considered as static friction ? 

$Assertion$ : Angle of repose is equal to the angle of limiting friction.
$Reason$ : When the body is just at the point of motion, the force of friction in this stage is called limiting friction.

Given in the figure are two blocks $A$ and $B$ of weight $20\, N$ and $100\, N$, respectively. These are being pressed against a wall by a force $F$ such that the system does not slide as shown. If the coefficient of friction between the blocks is $0.1$ and between block $B$ and the wall is $0.15$, the frictional force applied by the wall on block $B$ is ........ $N$

A uniform rod of length $L$ and mass $M$ has been placed on a rough horizontal surface. The horizontal force $F$ applied on the rod is such that the rod is just in the state of rest. If the coefficient of friction varies according to the relation $\mu = Kx$ where $K$ is a $+$ ve constant. Then the tension at mid point of rod is