$A$ man is pulling on a rope attached to a block on a smooth horizontal table. The tension in the rope will be the same at all points:

In the arrangement shown in the figure,the pulleys are massless and frictionless,and the threads are inextensible. The block of mass $m_1$ will remain at rest,if

Two masses of $5\, kg$ and $3\, kg$ are suspended with the help of massless inextensible strings as shown in the figure. The whole system is moving upwards with an acceleration of $2\, ms^{-2}$. The tensions $T_1$ and $T_2$ are respectively (Take $g = 10\, ms^{-2}$)

The pulley arrangements shown in the figure are identical, and the mass of the rope is negligible. In case $I$, the mass $m$ is lifted by attaching a mass $2m$ to the other end of the rope. In case $II$, the mass $m$ is lifted by pulling the other end of the rope with a constant downward force $F = 2mg$, where $g$ is the acceleration due to gravity. The acceleration of mass $m$ in case $I$ is

The ideal mechanical advantage of the combination of pulleys shown is

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