$A$ vessel containing water is given a constant acceleration $a$ towards the right,along a straight horizontal path. Which of the following diagrams represents the surface of the liquid?

$A$ boy of $50 \, kg$ is in a lift moving down with an acceleration of $9.8 \, m/s^2$. The apparent weight of the boy is ........... $N$ $(g = 9.8 \, m/s^2)$.

In the given arrangement,all surfaces are smooth. What acceleration $a$ should be given to the system (block $M$) so that the block $m_2$ does not slide down?

$A$ car is moving on a circular horizontal track of radius $10 \, m$ with a constant speed of $10 \, m/s$. $A$ plumb bob is suspended from the roof of the car by a light rigid rod of length $1.00 \, m$. The angle made by the rod with the vertical is ........ $^o$.

$A$ 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

$A$ 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 $g = 10 \text{ m/s}^2$)