$A$ 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 ........ $N$.

$A$ uniform metal chain is placed on a rough table such that one end of the chain hangs down over the edge of the table. When one-third of its length hangs over the edge,the chain starts sliding. Then,the coefficient of static friction is

The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is $50\%$ more compared to the time taken by the same block on an identical inclined smooth plane. Both inclined planes are at $45^\circ$ with the horizontal. The coefficient of kinetic friction between the rough inclined surface and the block is . . . . . . .

Find the work done by friction if a $1 \, kg$ block reaches the end of an inclined plane of length $10 \, m$ and inclination $30^{\circ}$ with constant velocity.

$A$ block of mass $M$ is sliding down an inclined plane. An external force $F$ is applied vertically downwards on the block. The coefficient of static friction is $\mu_s$ and the coefficient of kinetic friction is $\mu_k$. The friction force acting on the block is:

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