For frictionless surfaces in given arrangement tension $T_2$ is :-

A wooden block of mass $5 \mathrm{~kg}$ rests on soft horizontal floor. When an iron cylinder of mass $25$ $\mathrm{kg}$ is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $0.1 \mathrm{~ms}^{-2}$. The action force of the system on the floor is equal to:

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

A block of mass $200\, g$ is kept stationary on a smooth inclined plane by applying a minimum horizontal force $F =\sqrt{ x }N$ as shown in figure. The value of $x =.....$

A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given ${m}=8 \,{kg}, {M}=16\, {kg}$

Assume all the surfaces shown in the figure to be frictionless.

A wooden wedge of mass $M$ and inclination angle $(\alpha)$ rest on a smooth floor. A block of mass $m$ is kept on wedge. A force $F$ is applied on the wedge as shown in the figure such that block remains stationary with respect to wedge. So, magnitude of force $F$ is