$A$ 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?

$A$ 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 $g = 10 \text{ m/s}^2$)

An object of mass $5\, kg$ is attached to the hook of a spring balance and the balance is suspended vertically from the roof of a lift. The reading of the spring balance when the lift is going up with an acceleration of $0.25\, m/s^2$ is ......... $N$ $(g = 10\, m/s^2)$

$A$ 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 $g = 10 \, m/s^2$)

$A$ block of mass $m$ is kept on a wedge of mass $M$,as shown in the figure,such that mass $m$ remains stationary with respect to the wedge. The magnitude of force $P$ is

$A$ container of mass $m$ is pulled by a constant force $F$. Inside the container,a second block of the same mass $m$ is placed,connected to the wall by a massless spring of constant $k$. Initially,the spring is at its natural length. Find the velocity of the container at the instant the compression in the spring is maximum for the first time.