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

$A$ smooth sphere of radius $R$ moves along a straight line with a constant acceleration $a = g$. $A$ particle is placed at the top of the sphere. It is released from there with zero velocity relative to the sphere. What will be its speed relative to the sphere as a function of the angle $\theta$ as the particle slides?

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 '$a$' = . . . . . . .

The weight of a man in a lift moving in an upward direction with an acceleration '$a$' is $660 \text{ N}$. When the lift moves in the downward direction with the same acceleration, his weight is found to be $380 \text{ N}$. The real weight of the man when the lift is at rest is: (in $\text{ N}$)

An elevator car whose floor-to-ceiling distance is $2.7\,m$ starts ascending with a constant acceleration of $1.2\,m/s^2$. After $2\,s$ of the start,a bolt falls from the ceiling of the car. The free fall time of the bolt is $(g=9.8\,m/s^2)$.

$A$ man of mass $80\, kg$ is standing in an elevator which is moving with an acceleration of $6\, m/s^2$ in the upward direction. The apparent weight of the man will be ......... $N$ $(g = 10\, m/s^2)$.