A $\vec F\,\, = \,\,\hat i\, + \,4\hat j\,$ acts on block shown. The force of friction acting on the block is :

The coefficient of friction $\mu $ and the angle of friction $\lambda $ are related as

A cyclist speeding at $18 \;km/h$ on a level road takes a sharp circular turn of radius $3\; m$ without reducing the speed. The co-efficient of static friction between the tyres and the road is $0.1$. Will the cyclist slip while taking the turn?

When a body slides down from rest along a smooth inclined plane making an angle of $45^o$ with the horizontal, it takes time $T$. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time $pT$, where $p$ is some number greater than $1$. Calculate the coefficient of friction between the body and the rough plane.

A block of mass $70\,kg$ is kept on a rough horizontal surface $(\mu = 0.4)$. A person is trying to pull the block by applying a horizontal force, but the block is not moving. The net contact force exerted by the surface on the block is $F$, then

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