Find the force $F$ required on the cart so that the $2 \ kg$ and $1 \ kg$ blocks remain stationary relative to the cart.

Three masses $M = 100 \, kg$,$m_{1} = 10 \, kg$,and $m_{2} = 20 \, kg$ are arranged in a system as shown in the figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. $A$ force $F$ is applied on the system so that the mass $m_{2}$ moves upward with an acceleration of $2 \, m/s^{2}$. The value of $F$ is $...... \, N$. (Take $g = 10 \, m/s^{2}$)

$A$ person standing on a spring balance inside a stationary lift measures $60 \, kg$. The weight of that person if the lift descends with a uniform downward acceleration of $1.8 \, m/s^{2}$ will be $_{-} N$. $[g = 10 \, m/s^{2}]$

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

$A$ person of mass $50 \, kg$ stands on a weighing scale in a lift. If the lift is descending with a downward acceleration of $9 \, m/s^2$,what would be the reading of the weighing scale (in $, kg$)? (Take $g = 10 \, m/s^2$)

The weight of a man in a lift moving upward is $608 \ N$,while the weight of the same man in the lift moving downward with the same acceleration is $368 \ N$. His normal weight is ............ $N$.