The ends of a rope are held by two men who pull on it with equal and opposite forces of magnitude $F$ each. Then the tension in the rope is

$A$ lift is tied with thick iron ropes having mass $M$. The maximum acceleration of the lift is $a \ m/s^2$ and the maximum safe stress is $S \ N/m^2$. The minimum diameter of the rope is

$A$ $4 \text{ kg}$ mass is suspended as shown in the figure. All pulleys are frictionless and the spring constant $K$ is $8 \times 10^3 \text{ Nm}^{-1}$. The extension in the spring is $\left(g=10 \text{ ms}^{-2}\right)$.

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

If all the pulleys are massless and the string is ideal,find the reading of the spring balance.

An arrangement of a spring,strings,a pulley,and masses is shown in the figure below. The pulley and the strings are massless and $M > m$. The spring is light with spring constant $k$. If the string connecting $m$ to the ground is detached,then immediately after detachment,