$A$ ball falls freely from a height of $180 \,m$ onto a hard horizontal floor and repeatedly bounces. If the coefficient of restitution is $0.5$, the average speed and average velocity of the ball before it ceases to rebound are respectively (acceleration due to gravity $= 10 \,ms^{-2}$)

An engine is attached to a wagon through a shock absorber of length $1.5\, \text{m}$. The system with a total mass of $40,000\, \text{kg}$ is moving with a speed of $72\, \text{km/h}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest,the spring of the shock absorber gets compressed by $1.0\, \text{m}$. If $90\, \%$ of the energy of the wagon is lost due to friction,the spring constant is $....\, \times 10^{5}\, \text{N/m}$.

$A$ block of mass $M = 1 \ kg$ is released from rest at the top of a smooth track of radius $R = 40 \ m$. The block slides along the track without toppling,and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point $Q$ (where the radius makes an angle of $30^{\circ}$ with the horizontal),as shown in the figure,is $150 \ J$. (Take the acceleration due to gravity,$g = 10 \ m s^{-2}$)
$1.$ The speed of the block when it reaches the point $Q$ is:
$(A) 5 \ m s^{-1}$ $(B) 10 \ m s^{-1}$ $(C) 10\sqrt{3} \ m s^{-1}$ $(D) 20 \ m s^{-1}$
$2.$ The magnitude of the normal reaction that acts on the block at the point $Q$ is:
$(A) 7.5 \ N$ $(B) 8.6 \ N$ $(C) 11.5 \ N$ $(D) 22.5 \ N$
Give the answers for question $1$ and $2$.

$A$ ball is falling freely from a height. When it reaches $10 ~m$ height from the ground,its velocity is $v_0$. It collides with the ground,loses $50 \%$ of its energy,and rises back to a height of $10 ~m$. Then the velocity $v_0$ is (in $~m / s$)

Fill in the blanks:
$(a)$ In electricity consumption,$1$ unit is equal to .......... Joules of work.
$(b)$ $A$ body falling from a height of $10 \ m$ onto hard ground loses $20 \%$ of its energy. It can reach a height of .............
$(c)$ $A$ particle moves in a circular path of radius $a$ under the influence of an attractive force with potential energy $U = -\frac{k}{2r^2}$. Its total energy is = .......
$(d)$ Converting a mass of $1 \ \mu g$ into energy yields ........ energy.

$A$ block of mass $1 \ kg$ is placed at point $A$ on a rough path. It is gently pushed to the right. It slides down the slope and reaches point $B$. Find the work done by the friction force on the block during the journey from point $A$ to point $B$ in $J$. (Assume the vertical height difference between $A$ and $B$ is $0.2 \ m$ and the block starts and ends at rest).