$A$ body of mass $10 \ kg$ slides along a rough horizontal surface. The coefficient of friction is $1/\sqrt{3}$. Taking $g = 10 \ m/s^2$,the least force which acts at an angle of $30^\circ$ to the horizontal is ...... $N$.

In the figure shown,a block of weight $10 \, N$ is resting on a horizontal surface. The coefficient of static friction between the block and the surface is ${\mu _s} = 0.4$. $A$ force of $3.5 \, N$ will keep the block in uniform motion,once it has been set in motion. If a horizontal force of $3 \, N$ is applied to the block,then the block will:

What is the maximum acceleration of a train such that a $50 \ kg$ box lying on its floor remains stationary (in $m \ s^{-2}$)? (Given: Coefficient of static friction between the box and the train's floor is $0.3$ and $g = 10 \ m \ s^{-2}$)

The limiting friction is

$A$ 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

$A$ block placed on a rough horizontal surface is pulled by a horizontal force $F$. Let $f$ be the force applied by the rough surface on the block. Plot a graph of $f$ versus $F$.