For the pulley system shown in the figure,calculate the kinetic energy of the $6\,kg$ block after $5\,s$. (Assume $g = 10\,m/s^2$)

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:

Three identical blocks of masses $m = 2\; kg$ are pulled by a force $F = 10.2\; N$ with an acceleration of $0.6\; m/s^2$ on a frictionless surface. What is the tension (in $N$) in the string between the blocks $B$ and $C$?

$A$ 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 ........

In the arrangement shown,the mass $m$ will ascend with an acceleration (Pulley and rope are massless).

In the arrangement shown in the figure,the pulleys are massless and frictionless,and the threads are inextensible. The block of mass $m_1$ will remain at rest,if