In the arrangement shown,the pulleys are fixed and ideal,the strings are light,$m_1 > m_2$ and $S$ is a spring balance which is itself massless. The reading of $S$ (in units of mass) is

In order to raise a mass of $100\,kg$,a man of mass $60\,kg$ fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration $5g/4$ relative to the rope. The tension in the rope is ....... $N$. $(g = 10\,m/s^2)$

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.

$A$ uniform chain of length $2L$ is hanging in equilibrium over a small,smooth pulley. If end $B$ is given a slightly downward displacement $x$,the imbalance causes an acceleration. The acceleration of the chain when it has been displaced by distance $x$ is:

$A$ block of mass $1\,kg$ is suspended by a string of mass $1\,kg$ and length $1\,m$ as shown in the figure. Given $g = 10\,m/s^2$,calculate the tension in the string at its mid-point. (in $,N$)

$A$ block of mass $10 \ kg$ is placed on a horizontal frictionless surface and is attached to a cord which passes over two light frictionless pulleys as shown in the figure. The hanging block tied to the other end of the cord is initially at rest $2 \ m$ above the horizontal floor. If the hanging block strikes the floor $2 \ s$ after the system is released,then the weight of the hanging block is ....... $(g=10 \ ms^{-2})$ (in $N$)