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 trolley is falling freely on inclined plane as shown in the figure. The angle of string of pendulum with the ceiling of trolley is $(\alpha)$ equal to ..........

Two blocks $A$ and $B$ of masses $3\,m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut, are respectively

A book of mass $5 \,kg$ is placed on a table and it is pressed by $10 \,N$ force then normal force exerted by the table on the book is ......... $N$

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 $x =.....$