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

For the given system,the acceleration of the system is ........... $m/s^2$.

Three masses of $1\, kg$,$6\, kg$,and $3\, kg$ are connected to each other with threads and are placed on a table as shown in the figure. The acceleration with which the system is moving is $....... \, ms^{-2}$. (Take $g = 10\, ms^{-2}$)

$A$ light string fixed at one end to a clamp on the ground passes over a fixed pulley and hangs on the other side. It makes an angle of $30^{\circ}$ with the ground. $A$ monkey of mass $5 \ kg$ climbs up the rope. The clamp can tolerate a vertical force of $40 \ N$ only. The maximum acceleration in the upward direction with which the monkey can climb safely is ............ $m/s^2$ (neglect friction and take $g = 10 \ m/s^2$).

In the system shown in the figure,the pulleys and strings are ideal. Find the acceleration of $m_1$ with respect to $m_2$ $(m_1 = 2\ kg, m_2 = 2\ kg)$.

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$,the net force on the particle (directed towards the centre) is ($T$ is the tension in the string).