$A$ body of mass $2 \, kg$ is hung on a spring balance mounted vertically in a lift. If the lift descends with an acceleration equal to the acceleration due to gravity $g$,the reading on the spring balance will be ....... $kg$.

$A$ 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

$A$ pendulum of mass $m$ hangs from a support fixed to a trolley. The direction of the string when the trolley rolls up an inclined plane of inclination $\alpha$ with acceleration $a_0$ is (the string and bob remain fixed with respect to the trolley):

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 ............ $N$.

$A$ vehicle is moving with a constant speed of $10 \ m/s$ on a circular horizontal track of radius $20 \ m$. $A$ bob is suspended from the roof of the vehicle by a massless string. The angle made by the string with the vertical will be (acceleration due to gravity,$g = 10 \ m/s^2$).

$A$ 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?