If a body of mass $m$ is carried by a lift moving with an upward acceleration $a$,then the forces acting on the body are:
$(i)$ The reaction $R$ on the floor of the lift acting upwards.
$(ii)$ The weight $mg$ of the body acting vertically downwards.
The equation of motion will be given by:

$A$ man weighs $80\,kg.$ He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of $5\,m/s^2.$ What would be the reading on the scale? $(g = 10\,m/s^2)$ ............ $N$

$A$ person of $60 \,kg$ mass is in a lift which is coming down such that the man exerts a force of $150 \,N$ on the floor of the lift. Then the acceleration of the lift is $\left(g=10 \,ms^{-2}\right)$ (in $\,ms^{-2}$)

$A$ spring balance is attached to the ceiling of a lift. $A$ man hangs his bag on the spring and the spring reads $49 \, N$,when the lift is stationary. If the lift moves downward with an acceleration of $5 \, m/s^2$,the reading of the spring balance will be .......... $N$.

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 $(g=9.8\,m/s^2)$.

$A$ 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: