Two unequal masses are connected on two sides of a light string passing over a light and smooth pulley as shown in the figure. The system is released from rest. The larger mass $(2\, kg)$ is stopped $1\, s$ after the system is set into motion and then released. Find the time elapsed before the string becomes tight again. (Take $g = 10\, m/s^2$)

If the mass of block $B$ is $3\,kg$ and the mass of block $A$ is $7\,kg$,then the acceleration of the system is ........... $m/s^2$. $(g = 10\,m/s^2)$

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the center $P$ (as shown in the figure). Now,the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result,the particles move towards each other on the surface. The magnitude of acceleration,when the separation between them becomes $2x$ is

In order to test the strength of a rope,one end is tied to a large tree and the other end is hitched to a team of $2$ horses. The horses pull as hard as they can,but cannot break the rope. If the rope is untied from the tree and attached to another team of $2$ horses with equal strength,and the two teams pull in opposite directions,the tension in the rope will

When the system is allowed to fall freely,the tension in the string between the $10 \, kg$ and $5 \, kg$ masses is .......... $N$.

If the system is in equilibrium,what should be the tension in the rope?