What is the minimum acceleration with which a person can slide down a rope,if the breaking strength of the rope is $\frac{2}{3}$ of the person's weight?

$A$ steel block of $10\, \text{kg}$ rests on a horizontal floor. When three iron cylinders,each of mass $20\, \text{kg}$,are placed on it as shown,the entire system (block + cylinders) moves downward with an acceleration of $0.2\, \text{m/s}^2$. The normal reaction $R$ exerted by the floor is ..... $\text{N}$. [Take $g = 10\, \text{m/s}^2$]

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:

$A$ rope of mass $5 \,kg$ is moving vertically in a vertical position with an upward force of $100 \,N$ acting at the upper end and a downward force of $70 \,N$ acting at the lower end. The tension at the midpoint of the rope is ......... $N$.

$A$ cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is

$A$ 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