$A$ 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:

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 blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M = 2m$,then the stress produced in the wire is

An arrangement of a spring,strings,a pulley,and masses is shown in the figure below. The pulley and the strings are massless and $M > m$. The spring is light with spring constant $k$. If the string connecting $m$ to the ground is detached,then immediately after detachment,

$A$ hanging mass $M$ is connected to a four times larger mass $(4M)$ by using a string-pulley arrangement as shown in the figure. The larger mass is placed on a horizontal ice slab and is being pulled by a $2Mg$ force. In this situation,the tension in the string is $\frac{x}{5}Mg$. Find the value of $x$. Neglect the mass of the string and the friction between the block (larger mass) and the ice slab. (Given $g$ = acceleration due to gravity)

$A$ 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