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

Three blocks of mass $5 \ kg$ each are suspended from a ceiling as shown in the figure. The value of $\frac{T_3}{T_1}$ is .............

$A$ 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 $10 \,m$]

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

Two bodies of mass $4\,kg$ and $6\,kg$ are attached to the ends of a string passing over a pulley. The $4\,kg$ mass is also attached to the ground by another string. The tension $T_1$ in this lower string is equal to ......... $N$ (Take $g = 9.8\,m/s^2$)

$A$ light string passing over a smooth light fixed pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $g / 8$,then the ratio of masses is