The ends of a rope are held by two men who pull on it with equal and opposite forces of magnitude $F$ each. Then the tension in the rope is

$A$ 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 blocks $A$ and $B$, each of mass $20 \,kg$, lying on a frictionless table, are connected by a light string. The system is pulled horizontally with an acceleration of $2 \,ms^{-2}$ by a force $F$ applied on block $B$. The tension in the string will be: (in $\,N$)

$A$ uniform chain of length $2L$ is hanging in an equilibrium position. If end $B$ is given a slightly downward displacement,the imbalance causes an acceleration. Here,the pulley is small and smooth,and the string is inextensible. Find the velocity $v$ of the chain when it slips out of the pulley (height of pulley from floor $> 2L$).

An inextensible string passing over a smooth pulley connects two blocks of masses $m_1$ and $m_2$ $(m_2 > m_1)$ vertically. If the acceleration of the system is $(\frac{g}{n})$, then the ratio of masses $(\frac{m_2}{m_1})$ is

Two masses $M_1$ and $M_2$ are accelerated uniformly on a frictionless surface as shown in the figure. The ratio of the tensions $T_1/T_2$ is: