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

Three masses $M = 100 \, kg$,$m_{1} = 10 \, kg$,and $m_{2} = 20 \, kg$ are arranged in a system as shown in the figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. $A$ force $F$ is applied on the system so that the mass $m_{2}$ moves upward with an acceleration of $2 \, m/s^{2}$. The value of $F$ is $...... \, N$. (Take $g = 10 \, m/s^{2}$)

$A$ 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

$A$ block can slide on a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with a retardation $a$,the acceleration of the block relative to the incline is

$A$ person sitting inside an elevator performs a weighing experiment with an object of mass $50 \ kg$. Suppose that the variation of the height $y$ (in $m$) of the elevator,from the ground,with time $t$ (in $s$) is given by $y = 8[1 + \sin(\frac{2 \pi t}{T})]$,where $T = 40 \pi \ s$. Taking acceleration due to gravity,$g = 10 \ m/s^2$,the maximum variation of the object's weight (in $N$) as observed in the experiment is $.....$ .

An elevator is moving vertically up with an acceleration $a$. The force exerted on the floor by a passenger of mass $m$ is: