$A$ block is placed on a rough inclined plane of inclination $\theta = 30^o$. If the force required to drag it up along the plane is to be smaller than the force required to lift it vertically,the coefficient of friction $\mu$ should be less than:

$A$ board is balanced on a rough horizontal semicircular log. Equilibrium is obtained with the help of the addition of a weight to one of the ends of the board when the board makes an angle $\theta$ with the horizontal. The coefficient of friction between the log and the board is:

$A$ block of mass $5 \, kg$ is placed on a rough inclined plane with an angle of $30^\circ$. If the block moves down with a constant velocity,what is the coefficient of friction? (Take $g = 10 \, m/s^2$)

An insect is at the bottom of a hemispherical ditch of radius $R = 1\, m$. It crawls up the ditch but starts slipping after it is at height $h$ from the bottom. If the coefficient of friction between the ground and the insect is $\mu = 0.75$,then $h$ is $.......\, m$. $(g = 10\, m s^{-2})$

When a body slides down from rest along a smooth inclined plane making an angle of $45^{\circ}$ 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 is seen to take time $pT$,where $p$ is some number greater than $1$. Calculate the coefficient of friction between the body and the rough plane.

$A$ block of mass $5 \text{ kg}$ is placed on a rough inclined surface as shown in the figure. If $\vec{F}_1$ is the force required to just move the block up the inclined plane and $\vec{F}_2$ is the force required to just prevent the block from sliding down,then the value of $|\vec{F}_1|-|\vec{F}_2|$ is: [Use $g=10 \text{ m/s}^2$]