$A$ block of mass $2 \, kg$ rests on a plane inclined at an angle of $30^o$ with the horizontal. The coefficient of friction between the block and the surface is $0.7$. The frictional force acting on the block is . . . . . . $N$.

$A$ uniform chain of total length $L$ is at rest,partially on an incline of angle $\theta = 30^{\circ}$ and partially hanging vertically. The coefficient of friction between the chain and the incline is $\mu = \frac{1}{2\sqrt{3}}$. Find the ratio $\frac{L_{\max}}{L_{\min}}$,where $L_{\max}$ is the maximum length of the chain on the incline and $L_{\min}$ is the minimum length of the chain on the incline such that the chain remains at rest.

The tension $T$ in the string shown in the figure is:

$A$ block of mass $m$ is lying on an inclined plane. The coefficient of friction between the plane and the block is $\mu$. The force $(F)$ required to move the block up the inclined plane will be

$A$ block of mass $15\,kg$ is resting on a rough inclined plane as shown in the figure. The block is tied up by a horizontal string which has a tension of $50\,N$. The coefficient of friction between the surface of contact is: $(g = 10\,m/s^2)$

$A$ person climbs up a conveyor belt with a constant acceleration. The speed of the belt is $\sqrt{\frac{g h}{6}}$ and the coefficient of friction is $\frac{5}{3 \sqrt{3}}$. The time taken by the person to reach from $A$ to $B$ with the maximum possible acceleration is