$A$ uniform thick string of length $8\, m$ is resting on a horizontal frictionless surface. It is pulled by a horizontal force of $8\, N$ from one end. The tension in the string at $3\, m$ from the force applied is ........ $N$.

$A$ mass of $1 \ kg$ is suspended by means of a thread. The system is
$(i)$ lifted up with an acceleration of $4.9 \ ms^{-2}$
(ii) lowered with an acceleration of $4.9 \ ms^{-2}$.
The ratio of tension in the first and second case is

Two rectangular blocks of masses $40 \ kg$ and $60 \ kg$ are connected by a string and kept on a frictionless horizontal table. If a force of $1000 \ N$ is applied on the $60 \ kg$ block away from the $40 \ kg$ block,then the tension in the string is: (in $N$)

$A$ small ball $B$ of mass $m$ is suspended with a light inelastic string of length $L$ from a block $A$ of the same mass $m$,which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by an angle $\theta$ from the equilibrium position and then released. The maximum velocity of the block during the subsequent motion of the system after the release of the ball is

$A$ man slides down a light rope whose breaking strength is $\eta$ times the weight of the man $(\eta < 1)$. What is the maximum acceleration of the man so that the rope does not break?

Two bodies of masses $10\; kg$ and $20\; kg$ respectively,kept on a smooth horizontal surface,are tied to the ends of a light string. $A$ horizontal force $F = 600\; N$ is applied to $(i)\; A$,$(ii)\; B$ along the direction of the string. What is the tension in the string in each case?