If $300\,J$ of work is done to move a $2\,kg$ block up a rough inclined plane to a height of $10\,m$,find the work done against friction in $J$. (Take $g = 10\,m/s^2$)

$A$ body is sliding down a rough inclined plane. The coefficient of friction between the body and the plane is $0.5$. The ratio of the net force required for the body to slide down and the normal reaction on the body is $1:2$. Then the angle of the inclined plane is (in $^{\circ}$)

$A$ block of mass $m$ is at rest on an inclined plane with an angle of inclination $\theta$ and coefficient of friction $\mu$,as shown in the figure. The frictional force acting on the block is:

$A$ rough inclined plane is placed on a car moving with a constant velocity $u$ on horizontal ground. $A$ block of mass $M$ rests on the inclined plane. Is any work done by the force of friction between the block and the inclined plane? Is there any dissipation of energy?

$A$ cube of side length $a$ is resting on an inclined plane. What must be the value of the coefficient of friction $\mu$ between the cube and the plane so that the cube topples before sliding?

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ so that the insect does not slip is given by