$A$ monkey of mass $m$ is climbing a rope hanging from the roof with acceleration $a$. The coefficient of static friction between the body of the monkey and the rope is $\mu$. Find the direction and value of the friction force on the monkey.

$A$ uniform rope of mass $1.0 \ kg$ is connected to a box of mass $2.0 \ kg$,which is placed on a smooth horizontal surface. The free end of the rope is pulled horizontally by a force of $6 \ N$. Find the tension at the midpoint of the rope. ............ $N$

Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface as shown in the figure. The tension in the string will be

$A$ rope of length $L$ and mass $M$ is pulled by a constant force $F$ on a frictionless surface. What is the tension in the rope at a distance $x$ from the end where the force is applied?

$A$ steel block of $10\, \text{kg}$ rests on a horizontal floor. When three iron cylinders,each of mass $20\, \text{kg}$,are placed on it as shown,the entire system (block + cylinders) moves downward with an acceleration of $0.2\, \text{m/s}^2$. The normal reaction $R$ exerted by the floor is ..... $\text{N}$. [Take $g = 10\, \text{m/s}^2$]

The maximum tension a rope can withstand is $60 \,kg$-wt. The ratio of maximum acceleration with which two boys of masses $20 \,kg$ and $30 \,kg$ can climb up the rope at the same time is