With what minimum acceleration can a fireman slide down a rope if the breaking strength of the rope is $\frac{2}{3}$ of his weight?

Ten one-rupee coins are placed on top of each other on a table. Each coin has mass $m$. The reaction force of the $6^{th}$ coin (counted from the bottom) on the $7^{th}$ coin is .......... $mg$.

The mass of the lift is $200 \ kg$. When it ascends with an acceleration of $4 \ m/s^2$,the tension in the cable supporting the lift will be [Given: Acceleration due to gravity $g = 10 \ m/s^2$]. (in $N$)

For the given arrangement of blocks on a frictionless surface,the tension $T_2$ is:

Three identical particles are joined together by a thread as shown in the figure. All the three particles are moving on a smooth horizontal plane about point $O$. If the speed of the outermost particle is $v_0$,then the ratio of tension in the three sections of the thread 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 $N$)