Three blocks of masses $m$,$2m$,and $3m$ are pushed with a force $F$ across a frictionless table as shown in the figure. Let $N_{1}$ be the contact force between the left two blocks ($m$ and $2m$) and $N_{2}$ be the contact force between the right two blocks ($2m$ and $3m$). Then:

$A$ block of mass $M$ is placed on a horizontal surface and it is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. If $\mu < \mu_{min}$ (the minimum friction required to keep the block $m$ stationary),then the downward acceleration of $m$ is:

$A$ uniform thick string of length $5\,m$ is resting on a horizontal frictionless surface. It is pulled by a horizontal force of $5\,N$ from one end. The tension in the string at $1\,m$ from the force applied is ......... $N$.

An elevator weighing $6000\,kg$ is pulled upward by a cable with an acceleration of $5\,ms^{-2}$. Taking $g$ to be $10\,ms^{-2}$,the tension in the cable is ............ $N$.

Two particles each of mass $m$ are moving in horizontal circles with the same angular speed $\omega$. If both strings are of the same length $l$,find the ratio of tension in the strings $\frac{T_1}{T_2}$.

Two particles of equal mass $m$ are connected to a rope $AB$ of negligible mass such that one is at end $A$ and the other divides the length of the rope in the ratio $1:2$ from $B$. The rope is rotated about end $B$ in a horizontal plane. The ratio of the tension in the smaller part (between $B$ and the middle particle) to the tension in the larger part (between the two particles) is (ignore the effect of gravity).