$A$ uniform rope of total length $l$ is at rest on a table with a fraction $f$ of its length hanging (see figure). If the coefficient of friction between the table and the rope is $\mu$,then:

$A$ child weighing $25 \,kg$ slides down a rope hanging from a branch of a tall tree. If the force of friction acting against him is $200 \,N$,the acceleration of the child is ........... $m/s^2$ $\left(g=10 \,m/s^2\right)$.

Two blocks $A$ and $B$ of masses $2 \ kg$ and $4 \ kg$ respectively are kept on a rough horizontal surface. If the same force of $20 \ N$ is applied on each block,then the ratio of the accelerations of the blocks $A$ and $B$ is (Coefficient of kinetic friction between the surface and the blocks is $0.3$ and acceleration due to gravity $= 10 \ m \ s^{-2}$).

$A$ block of mass $10 \, kg$ is placed on a rough horizontal surface having a coefficient of friction $\mu = 0.5$. If a horizontal force of $100 \, N$ is acting on it,then the acceleration of the block will be ....... $m/s^2$.

"When a man walks on a rough surface,the frictional force acts in the direction opposite to his motion." Is this statement correct? Give reasons.

$A$ bag is gently dropped on a conveyor belt moving at a speed of $2\,m/s$. The coefficient of friction between the conveyor belt and the bag is $0.4$. Initially,the bag slips on the belt before it stops slipping due to friction. The distance travelled by the bag on the belt during the slipping motion is $.....m$. [Take $g=10\,m/s^{-2}$]