Both the blocks shown in the figure have mass $m$ and are moving with constant velocity in the directions indicated. They are in a resistive medium which exerts an equal constant force $F$ on both blocks in the direction opposite to their velocity. The tension in the string connecting them is: (Neglect friction)

$A$ uniform metal chain of mass $m$ and length $L$ passes over a massless and frictionless pulley. It is released from rest with a part of its length $l$ hanging on one side and the rest of its length $L - l$ hanging on the other side of the pulley. At a certain point in time,when $l = \frac{L}{x}$,the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is ........

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 $g = 10\, ms^{-2}$)

Tension in the rope at the rigid support is ............ $N$ $\left(g=10 \,m / s ^2\right)$

If $m_1 = 4m_2$ and the acceleration of $m_1$ is $a$,find the tension $T$ in the string.

In the given figure,two masses $m_1$ and $m_2$ $(m_2 > m_1)$ are at rest in an equilibrium position. Find the tension in string $AB$.