$A$ ball is dropped from an elevator moving upward with acceleration '$a$' by a boy standing in it. What is the acceleration of the ball with respect to the boy and the ground respectively? [Take upward direction as positive]

$A$ circular table is rotating with an angular velocity of $\omega \text{ rad/s}$ about its axis (see figure). There is a smooth groove along a radial direction on the table. $A$ steel ball is gently placed at a distance of $1 \text{ m}$ on the groove. All the surfaces are smooth. If the radius of the table is $3 \text{ m}$,the radial velocity of the ball with respect to the table at the time the ball leaves the table is $x \sqrt{2} \omega \text{ m/s}$,where the value of $x$ is............

$A$ 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?

Two wooden blocks of masses $M$ and $m$ are placed on a smooth horizontal surface as shown in the figure. If a force $P$ is applied to the system as shown in the figure such that the mass $m$ remains stationary with respect to the block of mass $M$,then the magnitude of the force $P$ is

$A$ car is moving on a circular horizontal track of radius $10 \,m$ with a constant speed of $10 \,m/s$. $A$ bob is suspended from the roof of the car by a light wire of length $1.0 \,m$. The angle made by the wire with the vertical is (in rad)

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