Three blocks are connected as shown in the figure on a horizontal frictionless table. If $m_1 = 1 \, kg, m_2 = 8 \, kg, m_3 = 27 \, kg$ and $T_3 = 36 \, N$,then $T_2$ will be ............ $N$.

Two spheres $P$ and $Q$ of equal masses $m$ are attached to a string of total length $2\, m$ as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular velocity $\omega$. The distance $OP = 1\, m$ and $PQ = 1\, m$. What is the value of the ratio $\left( \frac{\text{Tension in the string between } P \text{ and } Q}{\text{Tension in the string between } O \text{ and } P} \right)?$

$A$ rope of mass $5 \,kg$ is moving vertically in a vertical position with an upward force of $100 \,N$ acting at the upper end and a downward force of $70 \,N$ acting at the lower end. The tension at the midpoint of the rope is ......... $N$.

$A$ mass of $10 \, g$ is suspended by a string and the entire system is falling with a uniform acceleration of $400 \, cm/s^2$. The tension in the string will be.......... $dyne$ $(g = 980 \, cm/s^2)$.

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 $\frac{T_1}{T_2}$.