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

The maximum static frictional force is

$A$ box of mass $2 kg$ is placed on the roof of a car. The box would remain stationary until the car attains a maximum acceleration. The coefficient of static friction between the box and the roof of the car is $0.2$ and $g=10 ms^{-2}$. This maximum acceleration of the car,for the box to remain stationary,is: (in $ms^{-2}$)

$A$ body of mass $10 \ kg$ slides along a rough horizontal surface. The coefficient of friction is $1/\sqrt{3}$. Taking $g = 10 \ m/s^2$,the least force which acts at an angle of $30^\circ$ to the horizontal is ...... $N$.

Is it possible to jump off a perfectly smooth surface? Why?

$A$ $10\, kg$ 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 $g = 10\, m/s^2$)