Two blocks of masses $1 \ kg$ and $2 \ kg$ are connected by a light rod and the system is slipping down a rough incline at an angle of $45^{\circ}$ with the horizontal. The coefficient of kinetic friction at both contacts is $0.4$. If the acceleration of the system is $\alpha \sqrt{2} \ m/s^2$, find the value of $\alpha$. (Use $g = 10 \ m/s^2$)

$A$ block of mass $M$ slides down a rough inclined plane with constant velocity. The angle made by the inclined plane with the horizontal is $\theta$. The magnitude of the contact force will be:

The minimum value of $F$ so that the block is in equilibrium is

$A$ body of mass $m$ is launched up on a rough inclined plane making an angle of $30^{\circ}$ with the horizontal. The coefficient of friction between the body and plane is $\frac{\sqrt{x}}{5}$. If the time of ascent is half of the time of descent,the value of $x$ is ..... .

An inclined plane of length $5.60 \ m$ making an angle of $45^{\circ}$ with the horizontal is placed in a uniform electric field $E = 100 \ V \ m^{-1}$. $A$ particle of mass $1 \ kg$ and charge $10^{-2} \ C$ is allowed to slide down from rest from the maximum height of the slope. If the coefficient of friction is $0.1$,the time taken by the particle to reach the bottom is . . . . . . .

$A$ mass of $4\; kg$ rests on a horizontal plane. The plane is gradually inclined until at an angle $\theta = 15^{\circ}$ with the horizontal,the mass just begins to slide. What is the coefficient of static friction between the block and the surface?