$A$ monkey of mass $20 \, kg$ climbs up a rope which can withstand a maximum tension of $25 \, kgf$. What is the maximum acceleration with which the monkey can climb up? (Take $g = 10 \, m/s^2$)

Two masses of $5\, kg$ and $3\, kg$ are suspended with the help of massless inextensible strings as shown in the figure. Calculate $T_1$ and $T_2$ when the whole system is moving upwards with an acceleration $a = 2\, m/s^2$ (use $g = 9.8\, m/s^2$).

$A$ block of mass $1 \, kg$ is suspended by a string of mass $1 \, kg$ and length $1 \, m$ as shown in the figure. Taking $g = 10 \, m/s^2$,calculate the force exerted by the support on the string. (in $, N$)

What will be the acceleration of the system and tension in the rope connecting $5\,kg$ and $1\,kg$ blocks?

$A$ block of mass $m$ slides down on a wedge of mass $M$ as shown in the figure. Let $\vec a_1$ be the acceleration of the wedge and $\vec a_2$ be the acceleration of the block with respect to the ground. $N_1$ is the normal reaction between the block and the wedge,and $N_2$ is the normal reaction between the wedge and the ground. Friction is absent everywhere. Select the incorrect alternative.

Two blocks of masses $2m$ and $m$ are placed on a smooth horizontal surface. $A$ force $F$ is applied on the $2m$ block towards the right,and the same force $F$ is applied on the $m$ block towards the left. What is the ratio of the contact forces between the two blocks in the two cases?