$A$ force $\vec{F}=\hat{i}+4 \hat{j} \, N$ acts on the block of mass $1 \, kg$ 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 (Take $g = 10 \, m/s^2$)

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 $, kg$)

$A$ $20\, kg$ 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

For a given mass,how does rolling friction compare to static friction and kinetic friction?

$A$ force $F = mg$ is acting on a block of mass $m$ as shown in the figure. The pushing of the block along the surface is possible if:

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