$A$ lift is accelerating downward with an acceleration $a$. $A$ man inside the lift throws a ball upward with an acceleration $a_0$ relative to the lift $(a_0 < a)$. What is the acceleration of the ball as observed by an observer on the Earth?

$A$ boy of $50 \, kg$ is in a lift moving down with an acceleration of $9.8 \, m/s^2$. The apparent weight of the boy is ........... $N$ $(g = 9.8 \, m/s^2)$.

An object of mass $2 \, kg$ is placed at rest in a frame $S_1$ moving with velocity $10 \hat{i} + 5 \hat{j} \, m/s$ and having acceleration $5 \hat{i} + 10 \hat{j} \, m/s^2$. The object is also seen by an observer standing in a frame $S_2$ moving with velocity $5 \hat{i} + 10 \hat{j} \, m/s$. Calculate the net force acting on the object with respect to the $S_2$ frame.

$A$ 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 .......... $N$.

$A$ person sitting inside an elevator performs a weighing experiment with an object of mass $50 \ kg$. Suppose that the variation of the height $y$ (in $m$) of the elevator,from the ground,with time $t$ (in $s$) is given by $y = 8[1 + \sin(\frac{2 \pi t}{T})]$,where $T = 40 \pi \ s$. Taking acceleration due to gravity,$g = 10 \ m/s^2$,the maximum variation of the object's weight (in $N$) as observed in the experiment is $.....$ .

Imagine a person standing on a weighing machine placed inside an elevator. The elevator first accelerates, then moves with a constant velocity, and finally decelerates to stop. The maximum and minimum weight recorded are $80 \ kg$ and $64 \ kg$, respectively. Find out the true mass of that person considering $g = 10 \ m/s^2$. (in $kg$)