$A$ man of mass $60 \ kg$ is standing on a platform of mass $40 \ kg$ as shown in the figure. What force should the man apply on the rope so that he accelerates upward with the platform with an acceleration of $2 \ m/s^2$ (in $N$)? (Take $g = 10 \ m/s^2$)

Two masses $m_1 = 10 \ kg$ and $m_2 = 6 \ kg$ are attached to a string which passes over a frictionless smooth pulley. The acceleration of the masses is .......... $m/s^2$. (Take $g = 10 \ m/s^2$)

$A$ monkey of mass $40 \,kg$ climbs up a rope,of breaking load $600 \,N$ hanging from a ceiling. If it climbs up the rope with the maximum possible acceleration,then the time taken by the monkey to climb up is .........$s$ [Length of rope is $10 \,m$]

When the system is allowed to fall freely,the tension in the string between the $10 \, kg$ and $5 \, kg$ masses is .......... $N$.

In the system shown in the figure,there is no friction anywhere. The block $C$ $(2 \, kg)$ moves down by a distance $x_0 = 10 \, cm$ with respect to the wedge $D$ $(4 \, kg)$ when the system is released from rest. The velocity of $A$ $(1 \, kg)$ with respect to $B$ $(1 \, kg)$ will be $(g = 10 \, m/s^2)$ ......... $m/s$.

Three masses $m_1 = 4 \text{ kg}$,$m_2 = 4 \text{ kg}$,and $m_3 = 6 \text{ kg}$ are suspended from a fixed smooth frictionless pulley as shown in the figure. The value of $T_1/T_2$ is . . . . . . . (Take $g = 10 \text{ m/s}^2$)