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

$A$ girl drops an apple from the window of a train which is moving on a straight track with speed increasing at a constant rate. The trajectory of the falling apple as seen by the girl is

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

$A$ rocket is moving in a gravity-free space with a constant acceleration of $2 \ ms^{-2}$ along the $+x$ direction (see figure). The length of a chamber inside the rocket is $4 \ m$. $A$ ball is thrown from the left end of the chamber in the $+x$ direction with a speed of $0.3 \ ms^{-1}$ relative to the rocket. At the same time,another ball is thrown in the $-x$ direction with a speed of $0.2 \ ms^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is:

$A$ man is standing in a lift which goes up and comes down with the same constant acceleration. If the ratio of the apparent weights in the two cases is $2 : 1$,then the acceleration of the lift is ......... $m/s^2$.

In a lift moving up with an acceleration of $5 \,m/s^2$, a ball is dropped from a height of $1.25 \,m$. The time taken by the ball to reach the floor of the lift is ... (nearly) $(g=10 \,m/s^2)$ (in $\,s$)