$A$ 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

$A$ block of mass $m$ is kept in an elevator which starts moving downward with an acceleration $a$ as shown in the figure. The block is observed by two observers $A$ and $B$ for a time interval $t_0$. The observer $B$ is on the ground (inertial frame). What is the work done by the pseudo force on the block as observed by observer $B$?

$A$ 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):

$A$ lift is moving down with an acceleration $a$. $A$ man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively:

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

$A$ wedge $Y$ with mass of $10 \text{ kg}$ has all frictionless surfaces,and the inclined surface makes an angle of $37^{\circ}$ with the horizontal. $A$ block $X$ with mass $2 \text{ kg}$ is placed at the highest point of the wedge as shown in the figure and is at rest. At $t=0$,the wedge $Y$ is pulled toward the right with a constant force $f$ of $24 \text{ N}$. Taking the block $X$ at rest at $t=0$,the time taken by it to slide down $8.8 \text{ m}$ on the slope,while $Y$ is in motion,is . . . . . . s. (Take $\tan(37^{\circ}) = 3/4$ and $g = 10 \text{ m/s}^2$)