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 $g = 10\,m/s^2$)

$A$ particle is placed at rest inside a hollow hemisphere of radius $R$. The coefficient of friction between the particle and the hemisphere is $\mu = \frac{1}{\sqrt{3}}$. The maximum height up to which the particle can remain stationary is

When a cube of side length $a$ is in limiting equilibrium on an inclined plane and it is about to topple,what is the coefficient of friction between the cube and the plane?

$A$ block of mass $m$ is stationary on a rough plane of mass $M$ inclined at an angle $\theta$ to the horizontal,while the whole setup is accelerating upwards at an acceleration $a$. If the coefficient of friction between the block and the plane is $\mu$,then the force that the plane exerts on the block is

$A$ body of mass $100\, g$ is sliding down an inclined plane of inclination $30^\circ$. What is the frictional force experienced if the coefficient of friction $\mu = 1.7$?

$A$ uniform chain of length $L$ hangs partly from a table and is kept in equilibrium by friction. If the maximum length of the chain that can hang without slipping is $l$,then the coefficient of friction between the table and the chain is: