Two blocks of mass $8\,kg$ and $2\,kg$ are connected by a string and they are released on an inclined plane of inclination $30^o$ as shown in the figure. What will be the tension in the string connecting the two blocks (in $,N$)? (Assume the surface is frictionless and $g = 10\,m/s^2$)

$A$ system of $10$ balls,each of mass $m = 2 \; kg$,is connected via a massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in the figure. Find the tension $T$ in the string between the $7^{th}$ and $8^{th}$ ball when the $6^{th}$ ball just leaves the table. (in $; N$)

The minimum acceleration with which a fireman can slide down a rope of breaking strength two-third of his weight 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

Two particles of equal mass $m$ are connected to a rope $AB$ of negligible mass such that one is at end $A$ and the other divides the length of the rope in the ratio $1:2$ from $B$. The rope is rotated about end $B$ in a horizontal plane. The ratio of the tension in the smaller part (between $B$ and the middle particle) to the tension in the larger part (between the two particles) is (ignore the effect of gravity).

Three blocks of masses $m_1, m_2$ and $m_3$ are connected by massless strings as shown on a frictionless table. They are pulled with a force $F = 40 \, N$. If $m_1 = 10 \, kg, m_2 = 6 \, kg$ and $m_3 = 4 \, kg$,the tension $T_2$ (between $m_1$ and $m_2$) will be ........ $N$.