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 .............

$A$ smooth massless string passes over a smooth fixed pulley. Two masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is

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 $g = 9.8\,m/s^2$)

If $m_1 = 4m_2$,and the acceleration of $m_1$ is $a$,then find $a$.

$A$ 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

Two masses $8\; kg$ and $12\; kg$ are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.