$A$ $20\, kg$ block is initially at rest on a rough horizontal surface. $A$ horizontal force of $75\, N$ is required to set the block in motion. After it is in motion,a horizontal force of $60\, N$ is required to keep the block moving with constant speed. The coefficient of static friction is

$A$ force $\vec{F} = \hat{i} + 4\hat{j} \text{ N}$ acts on the $1 \text{ kg}$ block shown in the figure. The coefficient of friction between the block and the surface is $\mu = 0.3$. The force of friction acting on the block is:

$A$ heavy body of mass $25 \ kg$ is to be dragged along a horizontal plane $\left( \mu = \frac{1}{\sqrt{3}} \right)$. The least force required is ........ $kgf$.

$A$ 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 $ms^{-2}$)

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

If ${\mu _s}$,${\mu _k}$,and ${\mu _r}$ are coefficients of static friction,sliding (kinetic) friction,and rolling friction respectively,then: