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 $\frac{T_1}{T_2}$.

The tension in the string connecting the blocks as shown in the figure is ............ $N$.

$A$ block of mass $m$ is kept on a platform which starts from rest with constant acceleration $g/2$ upward,as shown in the figure. Work done by the normal reaction on the block in time $t$ is

Three blocks of masses $2 \, kg, 3 \, kg$ and $5 \, kg$ are connected to each other with light strings and are placed on a frictionless surface as shown in the figure. The system is pulled by a force $F = 10 \, N$. Find the tension $T_1$ in the string between the $2 \, kg$ and $3 \, kg$ blocks. (in $, N$)

For the given figure,what will be the acceleration of the blocks and the tension in the string connecting the $2\,kg$ and $5\,kg$ blocks? (Assume $g = 10\,m/s^2$)

Three blocks $A, B$ and $C$ weighing $1 \, kg, 8 \, kg$ and $27 \, kg$ respectively are connected as shown in the figure with an inextensible string and are moving on a smooth surface. If ${T_3} = 36 \, N$,then find the value of ${T_2}$ in $N$.