$A$ block rests on a rough inclined plane making an angle of $30^o$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8$. If the frictional force on the block is $10 \, N$,the mass of the block (in $kg$) is (take $g = 10 \, m/s^2$)

$A$ homogeneous cubical brick lies motionless on a rough inclined surface. The half of the brick which applies greater pressure on the plane is:

$A$ body takes just twice the time to slide down a plane inclined at $30^\circ$ to the horizontal as it would if the plane were frictionless. The coefficient of friction between the body and the plane is:

$A$ block slides down an inclined plane of slope angle $\theta$ with a constant velocity. It is then projected up the plane with an initial velocity $u$. The distance up to which it will rise before coming to rest is

$A$ bob of mass $m$ is attached to a string of length $\ell$ whose other end is tied to a light vertical rod as shown in the figure. The bob is swinging in a horizontal plane with a constant angular speed $\omega$. The vertical rod is supported on a block of mass $M$ which is placed on a rough surface. What is the minimum friction coefficient between the ground and the block for which the block does not slip?

An insect is crawling in a hemispherical bowl of radius $R$. If the coefficient of friction between the insect and the bowl is $\mu$,then the maximum height to which the insect can crawl in the bowl is