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 $N$.

$A$ block of mass $48 \ kg$ kept on a smooth horizontal surface is pulled by a rope of length $4 \ m$ by a horizontal force of $25 \ N$ applied to the other end. If the linear density of the rope is $0.5 \ kg \ m^{-1}$,the force acting on the block is (in $N$)

$A$ block of mass $M$ on a horizontal smooth surface is pulled by a load of mass $M/2$ by means of a rope $AB$ and string $BC$ as shown in the figure. The length and mass of the rope $AB$ are $L$ and $M/2$ respectively. As the block is pulled from $AB = L$ to $AB = 0$,its acceleration changes from:

The mass of a lift is $2000 \, kg$. When the tension in the supporting cable is $28000 \, N$,then its acceleration is:

$T_1$ and $T_2$ in the given figure are

$A$ 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.......... $dyne$ $(g = 980 \, cm/s^2)$.