An ice cube is kept on an inclined plane of angle $30^{\circ}$. The coefficient of kinetic friction between the block and the inclined plane is $(1 / \sqrt{3})$. What is the acceleration of the block? $...... \ m / s ^2$

$A$ box is lying on an inclined plane. What is the coefficient of static friction if the box starts sliding when the angle of inclination is $60^\circ$?

$A$ disc arranged in a vertical plane has two grooves of the same length directed along the vertical chord $AB$ and the chord $CD$ as shown in the figure. Particles slide down along $AB$ and $CD$ starting from rest. The ratio of the time $t_{AB}/t_{CD}$ is

$A$ block of mass $8 \ kg$ is at rest on a rough inclined plane as shown in the figure. The magnitude of the net force exerted by the surface on the block will be $..... \ N$. (Take $g = 10 \ m/s^2$)

$A$ body of mass $10\, kg$ is lying on a rough plane inclined at an angle of $30^\circ$ to the horizontal,and the coefficient of friction is $0.5$. The minimum force required to pull the body up the plane is ........ $N$.

$A$ block of mass $m$ is placed on a wedge of angle $\theta$. The wedge is moving with a constant velocity $v$ on a horizontal surface. If the block does not slide on the wedge,find the work done by the friction force on the block in time $t$.