$A$ bullet of mass $m$ moving with velocity $v$ strikes a suspended wooden block of mass $M$. If the block rises to a height $h$,the initial velocity of the bullet will be

Two bodies $A$ and $B$ of masses $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring. $A$ third body $C$ of mass $m$ moves with velocity $V_0$ along the line joining $A$ and $B$ and collides elastically with $A$ as shown in the figure. At a certain instant of time $t_0$ after the collision,it is found that the instantaneous velocities of $A$ and $B$ are the same. Further,at this instant,the compression of the spring is found to be $x_0$. Determine the spring constant $k$.

$A$ block of mass $m$ starts at rest at height $h$ on a frictionless inclined plane. The block slides down the plane,travels across a rough horizontal surface with coefficient of kinetic friction $\mu$,and compresses a spring with force constant $k$ a distance $x$ before momentarily coming to rest. Then the spring extends and the block travels back across the rough surface,sliding up the plane. The block travels a total distance $d$ on the rough horizontal surface. The correct expression for the maximum height $h'$ that the block reaches on its return is

$A$ bob $B$ of mass $m$ at rest is hanging vertically from the ceiling via a massless string of length $10 \text{ m}$. $A$ point mass $A$ of mass $m$ travelling horizontally with speed $10 \text{ ms}^{-1}$ hits bob $B$ elastically. The bob $B$ rises $h$ meters after the collision. Taking the acceleration due to gravity $g = 10 \text{ ms}^{-2}$ and neglecting the size of the bob, the value of $h$ is:

Three blocks $A, B$ and $C$ are lying on a smooth horizontal surface,as shown in the figure. $A$ and $B$ have equal masses $m$,while $C$ has mass $M$. Block $A$ is given an initial speed $v$ towards $B$,due to which it collides with $B$ perfectly inelastically. The combined mass then collides with $C$,also perfectly inelastically. If $5/6^{th}$ of the initial kinetic energy is lost in the whole process,what is the value of $M/m$?

$A$ constant force of $5 N$ accelerates a stationary particle of mass $500 g$ through a displacement of $5 m$. The average power delivered is: (in $W$)