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

Two spheres $P$ and $Q$,each of mass $200 \text{ g}$,are attached to a string of length $1 \text{ m}$ as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that between $P$ and $O$ is (where $P$ is at the mid-point of the line joining $O$ and $Q$).

$A$ balloon carrying some sand of mass $M$ is moving down with a constant acceleration $a_0$. The mass $m$ of sand to be removed so that the balloon moves up with double the acceleration $2a_0$ is:

$A$ body of mass $8\,kg$ is hanging from another body of mass $12\,kg$. The combination is being pulled upwards by a string with an acceleration of $2.2\,m/s^2$. The tensions $T_1$ (in the top string) and $T_2$ (in the string between the two masses) will be respectively: (use $g = 9.8\,m/s^2$)

The mass of a lift is $500\, kg$. When it ascends with an acceleration of $2\, m/s^2$,the tension in the cable will be........... $N$ $[g = 10\, m/s^2]$

Two blocks,each of mass $M$,are initially at rest on frictionless surfaces as shown in the figure. If the pulleys are light and frictionless,and the block of mass $M$ on the incline is allowed to move down,then the tension in the string will be$-$