$A$ person in an elevator accelerating upwards with an acceleration of $2\,ms^{-2}$,tosses a coin vertically upwards with a speed of $20\,ms^{-1}$. After how much time will the coin fall back into his hand? (Take $g = 10\,ms^{-2}$)

$A$ 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 $m$ is kept in an elevator which starts moving downward with an acceleration $a$ as shown in the figure. The block is observed by two observers $A$ and $B$ for a time interval $t_0$. According to the observer $A$,which of the following is true?

In the figure,the reading of the spring balance will be $......\,N$ $\left[ g = 10\,m/s^2 \right]$.

$A$ mass is hanging on a spring balance which is kept in a lift. The lift ascends with an acceleration. The spring balance will show in its readings:

$A$ piece of wire is bent in the shape of a parabola $y=kx^2$ ($y$-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$-axis with a constant acceleration $a$. The distance of the new equilibrium position of the bead,where the bead can stay at rest with respect to the wire,from the $y$-axis is