$A$ block of mass $1 \, kg$ is suspended by a string of mass $1 \, kg$ and length $1 \, m$ as shown in the figure. Taking $g = 10 \, m/s^2$,calculate the force exerted by the support on the string. (in $, N$)

Two masses of $5 \,kg$ and $3 \,kg$ are suspended with the help of massless inextensible strings as shown in the figure below. When the whole system is moving upwards with an acceleration of $2 \,m/s^2$, the value of $T_1$ is (use $g = 9.8 \,m/s^2$): (in $\,N$)

$A$ car of mass $1000\,kg$ is moving at a speed of $30\,m/s.$ Brakes are applied to bring the car to rest. If the net retarding force is $5000\,N,$ the car comes to stop after travelling $d\,m$ in $t\,s.$ Then

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 $N$.

$A$ string tied to a roof can bear a maximum tension of $50 \,kg$ wt. The minimum acceleration with which a man of $98 \,kg$ can descend is ...... $m/s^2$ [Take $g = 9.8 \,m/s^2$].

$A$ 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 $N$)