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

$A$ 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 ........

$A$ particle of small mass $m$ is joined to a very heavy body of mass $M$ by a light string passing over a light pulley. Both bodies are free to move. The total downward force on the pulley is

Two masses of $1\, kg$ and $5\, kg$ are attached to the ends of a massless string passing over a pulley of negligible weight. The pulley itself is attached to a light spring balance as shown in the figure. When the masses are released and start moving,the reading of the spring balance will be:

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 $\,N$)

Two masses $m_1$ and $m_2$ are connected by a light string passing over a smooth pulley. When set free,$m_1$ moves downwards by $3 \ m$ in $3 \ s$. The ratio of $\frac{m_1}{m_2}$ is $(g = 10 \ ms^{-2})$.