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

$A$ $4 \text{ kg}$ mass is suspended as shown in the figure. All pulleys are frictionless and the spring constant $K$ is $8 \times 10^3 \text{ Nm}^{-1}$. The extension in the spring is $\left(g=10 \text{ ms}^{-2}\right)$.

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 ....... $N$. $(g = 10\,m/s^2)$

$A$ mass of $100\,kg$ is moved with uniform velocity under the influence of force $F$. Find the force acting on the beam due to the string connected to the ceiling 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 $> 2L$).

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 $\,N$)