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

$A$ movable steel plate is placed between fixed steel and brass plates and the stack of plates is subjected to a weight of $100 \ N$ as shown in the figure. The coefficient of kinetic friction for steel on steel is $0.57$ and for steel on brass is $0.44$. Assuming that the entire weight comes onto the stack and that the weight of the plates is negligible in comparison to the applied weight, the force required to move the middle plate (in $N$) is

$A$ conveyor belt is moving at a constant speed of $2\, m s^{-1}$. $A$ box is gently dropped on it. The coefficient of friction between them is $\mu = 0.5$. The distance that the box will move relative to the belt before coming to rest on it,taking $g = 10\, m s^{-2}$,is ........... $m$.

Two masses $m_1 = 10 \text{ kg}$ and $m_2 = 20 \text{ kg}$ are connected by an inextensible string over a frictionless pulley,as shown in the figure. The coefficient of friction of the horizontal surface is $\mu = 0.15$. The minimum mass $m$ that should be placed on top of $m_2$ to stop the motion is:

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

When two surfaces are coated with a lubricant,then they