You are holding a vertical cylindrical rod of mass $1 \, kg$ by pressing it (with a force of $12 \, N$) with two fingers. The coefficient of friction between the rod and the fingers is $\mu = 0.5$. The force of friction on the rod will be ........ $N$.

$A$ force $\vec{F}=\hat{i}+4 \hat{j}$ acts on the block shown in the figure. The force of friction acting on the block is (take $g=10 \, m/s^2$)

$A$ block of mass $3 \,kg$ is pressed against a vertical wall by applying a force $F$ at an angle $30^{\circ}$ to the horizontal as shown in the figure. As a result, the block is prevented from falling down. If the coefficient of static friction between the block and wall is $\mu = \sqrt{3}$, then the value of $F$ is (use $g=10 \,m/s^2$):

$A$ block of mass $5 \,kg$ is pulled by a force $F$ as shown in the figure. If the coefficient of friction is $0.1$, then the force needed to accelerate the block to $3 \,m/s^2$ to the right is close to (in $\,N$)

Which of the following is correct when a person walks on a rough surface?

$A$ block is kept on a rough horizontal surface. The acceleration of the block increases from $6 \ m/s^2$ to $11 \ m/s^2$ when the horizontal force acting on it increases from $20 \ N$ to $30 \ N$. The coefficient of kinetic friction between the block and the surface is (Acceleration due to gravity $g = 10 \ m/s^2$):