$A$ force of $19.6\, N$ when applied parallel to the surface just moves a body of mass $10\, kg$ kept on a horizontal surface. If a $5\, kg$ mass is kept on the first mass,the force applied parallel to the surface to just move the combined body is........ $N.$

$A$ block of mass $M$ is placed on a horizontal surface and it is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. If $\mu$ is the coefficient of friction between the block $M$ and the horizontal surface,then the minimum value of $m_0$ required to keep the block $m$ stationary is

$A$ box of mass $15 \text{ kg}$ is kept on the floor of a stationary trolley. The coefficient of static friction between the box and the trolley is $0.12$. Keeping the box in a stationary state over the trolley, the maximum acceleration with which the trolley can be moved horizontally in $\text{m s}^{-2}$ is: $(g = 10 \text{m s}^{-2})$

$A$ uniform chain of $6 \, m$ length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The coefficient of static friction between the chain and the surface of the table is $0.5$. The maximum length of the chain hanging from the table is.......$m.$

$A$ 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:

What can be inferred from the relation $f_S \leqslant \mu_S N$?