$A$ body takes time $t$ to reach the bottom of an inclined plane of angle $\theta$ with the horizontal. If the plane is made rough,the time taken now is $2t$. The coefficient of friction of the rough surface is

$A$ small block starts sliding down an inclined plane forming an angle $45^{\circ}$ with the horizontal. The coefficient of friction $\mu$ varies with distance $s$ as $\mu = C s^2$,where $C$ is a constant of appropriate dimensions. The distance covered by the block before it stops is:

When a body slides down from rest along a smooth inclined plane making an angle of $30^{\circ}$ with the horizontal,it takes time $T$. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance,it takes time $\alpha T$,where $\alpha$ is a constant greater than $1$. The coefficient of friction between the body and the rough plane is $\frac{1}{\sqrt{x}}\left(\frac{\alpha^{2}-1}{\alpha^{2}}\right)$ where $x = .....$.

$A$ block slides down on an inclined surface of inclination $30^{\circ}$ with the horizontal. Starting from rest,it covers $8 \ m$ in the first two seconds. Find the coefficient of friction. (Take $g = 10 \ m/s^2$)

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

$A$ block of a certain mass is placed on a rough inclined plane. The angle between the plane and the horizontal is $30^{\circ}$. The coefficients of static and kinetic friction between the block and the inclined plane are $0.6$ and $0.5$ respectively. Then,the magnitude of the acceleration of the block is [Take $g = 10 \ ms^{-2}$]