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 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 of mass $M_1 = 20\,kg$ and $M_2 = 12\,kg$ are connected by a metal rod of mass $8\,kg.$ The system is pulled vertically up by applying a force of $480\,N$ as shown. The tension at the mid-point of the rod is ........ $N$

Consider the following statements about the blocks shown in the diagram that are being pushed by a constant force on a frictionless table

$A.$All blocks move with the same acceleration

$B.$The net force on each block is the same

Which of these statements are/is correct

In the diagram shown, the normal reaction force between $2\,kg$ and $1\,kg$ is (Consider the surface, to be smooth)$.........N$ (Given $g =10\,ms ^{-2}$)

A perfect smooth sphere $A$ of mass $2\  kg$ is in contact with a rectangular block $B$ of mass $4\  kg$ and vertical wall as shown in the figure. All surfaces are smooth. Find normal reaction by vertical wall on sphere $A$  .......... $N$