An object of mass $m$ is being moved with a constant velocity under the action of an applied force of $2\, N$ along a frictionless surface with the following surface profile. The correct applied force vs distance graph will be:

When a body moves with some friction on a surface,

$A$ block of mass $m$ is lying on a rough inclined plane having an inclination $\alpha = \tan^{-1}(\frac{1}{5})$. The inclined plane is moving horizontally with a constant acceleration of $a = 2 \text{ ms}^{-2}$ as shown in the figure. The minimum value of the coefficient of friction,so that the block remains stationary with respect to the inclined plane,is (Take $g = 10 \text{ ms}^{-2}$):

Two blocks of masses in the ratio $m:n$ are connected by a light inextensible string passing over a frictionless fixed pulley. If the system of the blocks is released from rest, then the acceleration of the centre of mass of the system of the blocks is ($g$ = acceleration due to gravity).

An object of mass $M$ is placed on a rough horizontal surface (coefficient of friction $\mu$). $A$ person tries to pull the object by applying a horizontal force,but the object does not move. The force $F$ exerted by the surface on the object is:

In the figures $(i), (ii)$ and $(iii)$ shown, the objects $A, B$ and $C$ have the same mass $m$. The string, spring, and pulley are massless. Object $C$ strikes object $B$ with velocity $u$ in each case and sticks to it. Find the ratio of the velocity of $B$ in case $(i)$ to $(ii)$ to $(iii)$.