The ratio of the weight of a man in a stationary lift to his weight in a lift moving downwards with an acceleration '$a$' is $3:2$. Then '$a$' = . . . . . . .

$A$ plank is moving in a horizontal direction with a constant acceleration $a \hat{i}$. $A$ uniform rough cubical block of side $l$ rests on the plank and is at rest relative to the plank. Let the centre of mass of the block be at $(0, l/2)$ at a given instant. If $a = g/10$,then the normal reaction exerted by the plank on the block at that instant acts at

If the rope of a lift breaks suddenly,what is the tension exerted by the floor of the lift on a person inside? ($a =$ acceleration of the lift)

$A$ wedge $Y$ with mass of $10 \text{ kg}$ has all frictionless surfaces,and the inclined surface makes an angle of $37^{\circ}$ with the horizontal. $A$ block $X$ with mass $2 \text{ kg}$ is placed at the highest point of the wedge as shown in the figure and is at rest. At $t=0$,the wedge $Y$ is pulled toward the right with a constant force $f$ of $24 \text{ N}$. Taking the block $X$ at rest at $t=0$,the time taken by it to slide down $8.8 \text{ m}$ on the slope,while $Y$ is in motion,is . . . . . . s. (Take $\tan(37^{\circ}) = 3/4$ and $g = 10 \text{ m/s}^2$)

$A$ person is standing in an elevator. In which of the following situations does he find his weight to be less than his actual weight?

$A$ block of mass $m$ is kept on a wedge of mass $M$,as shown in the figure,such that mass $m$ remains stationary with respect to the wedge. The magnitude of force $P$ is