The friction coefficient between the horizontal surface and each of the blocks shown in the figure is $\mu = 0.2$. The collision between the blocks is perfectly elastic. What is the separation between the blocks when they come to rest? (in $cm$)

$A$ car travelling at a speed of $30 \, km/h$ is brought to a halt in $8 \, m$ by applying brakes. If the same car is travelling at $60 \, km/h$,it can be brought to a halt with the same braking force in ............... $m$.

Three particles $A, B$,and $C$ of equal mass move with speed $V$ as shown to strike at the centroid of an equilateral triangle. After the collision,$A$ comes to rest and $B$ retraces its path with speed $V$. The speed of $C$ after the collision is:

Morning breakfast provides $5000 \,cal$ of energy to a $60 \,kg$ person. The efficiency of the person is $30 \%$. The height up to which the person can climb using the energy obtained from the breakfast is ......... $m$.

Two bodies $A$ and $B$ of mass $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. $A$ third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision,it is found that the instantaneous velocities of $A$ and $B$ are the same and the compression of the spring is $x_0$. The spring constant $k$ will be

$A$ curved surface is shown in the figure. The portion $BCD$ is free of friction. There are three spherical balls of identical radii and masses. Balls are released from rest one by one from $A$,which is at a slightly greater height than $C$.
With the surface $AB$,ball $1$ has large enough friction to cause rolling down without slipping; ball $2$ has a small friction and ball $3$ has a negligible friction.
$(a)$ For which balls is total mechanical energy conserved?
$(b)$ Which ball$(s)$ can reach $D$?
$(c)$ For balls which do not reach $D$,which of the balls can reach back $A$?