If a body of mass $m$ is carried by a lift moving with an upward acceleration $a$,then the forces acting on the body are:
$(i)$ The reaction $R$ on the floor of the lift acting upwards.
$(ii)$ The weight $mg$ of the body acting vertically downwards.
The equation of motion will be given by:

$A$ body of mass $1.0 \, kg$ is falling with an acceleration of $10 \, m/s^2$. Its apparent weight will be ......... $kg \, wt$ $(g = 10 \, m/s^2)$.

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

Cream gets separated out of milk when it is churned,it is due to

$A$ ball is suspended on a thread from the ceiling of a car. The brakes are applied and the speed of the car changes from $5 \, m/s$ to $5/3 \, m/s$ during a time interval of $3 \, s$. Find the angle $\theta$ that the thread will deviate from the vertical.

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest,as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
To an observer $B$,when the block is compressing the spring: