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

$A$ small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force $mkv^{2}$ where $v$ is its speed. The maximum height attained by the ball is

Two blocks of masses $m$ and $2m$ kept on a frictionless horizontal surface are connected by a massless string. Two horizontal forces $F_1 = (4.2t) \text{ N}$ and $F_2 = (7.5t) \text{ N}$,where '$t$' is time in seconds,are acting on the system as shown in the figure. The time at which the tension in the string between the two blocks becomes $10.6 \text{ N}$ is $t$ seconds.

$A$ block of mass $48 \ kg$ kept on a smooth horizontal surface is pulled by a rope of length $4 \ m$ by a horizontal force of $25 \ N$ applied to the other end. If the linear density of the rope is $0.5 \ kg \ m^{-1}$,the force acting on the block is (in $N$)

Two blocks of mass $M_1 = 20\,kg$ and $M_2 = 12\,kg$ are connected by a metal rod of mass $8\,kg$. The system is pulled vertically up by applying a force of $480\,N$ as shown. The tension at the mid-point of the rod is ........ $N$.

Three blocks are connected as shown in the figure on a horizontal frictionless table. If $m_1 = 1 \, kg, m_2 = 8 \, kg, m_3 = 27 \, kg$ and $T_3 = 36 \, N$,then $T_2$ will be ............ $N$.