$A$ man weighing $60 \text{ kg}$ is in a lift moving down with an acceleration of $1.8 \text{ ms}^{-2}$. The force exerted by the floor on him is:

$A$ vessel containing water is moving with a constant speed towards the right along a straight horizontal path. If the vessel is given a constant retardation towards the right along a straight line,which of the following diagrams represents the surface of the liquid?

$A$ block of mass $m$ is placed on a smooth inclined wedge $ABC$ of inclination $\theta$ as shown in the figure. The wedge is given an acceleration $a$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is

$A$ solid sphere of mass $2\, kg$ is resting inside a cube as shown in the figure. The cube is moving with a velocity $\vec v = (5t\,\hat i + 2t\,\hat j)\,m/s$. Here $t$ is the time in seconds. All surfaces are smooth. The sphere is at rest with respect to the cube. Find the total force $N$ exerted by the sphere on the cube. (Take $g = 10\, m/s^2$)

$A$ body is thrown up in a lift with a velocity $u$ relative to the lift,and the time of flight is found to be $t$. The acceleration with which the lift is moving up is:

Two trolleys $A$ and $B$ are moving with accelerations $a$ and $2a$ respectively in the same direction. To an observer in trolley $A$,the magnitude of the pseudo force acting on a block of mass $m$ on trolley $B$ is