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

$A$ 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 ........

$A$ 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 $,N$)

$A$ mass $M$ is lowered by the help of a string at a constant acceleration of $\frac{g}{2}$ for a distance $x$. What is the work done by the string?

Two masses $M_{1}$ and $M_{2}$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_{2}$ is twice that of $M_{1}$,the acceleration of the system is $a_{1}$. When the mass $M_{2}$ is thrice that of $M_{1}$,the acceleration of the system is $a_{2}$. The ratio $\frac{a_{1}}{a_{2}}$ will be:

Two identical blocks each of mass $M$ are attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. $A$ small mass $m$ is now placed on block $B$ (the right block). The acceleration with which the two blocks move together is ($g =$ gravitational acceleration).