When a ball is freely fallen from a given height,it bounces to $80\%$ of its original height. What fraction of its mechanical energy is lost in each bounce?

$A$ simple pendulum of length $L = \frac{10}{3} \text{ m}$ with a bob of mass $M = 3m$ is hanging freely from a rigid support. $A$ bullet of mass $m$ is fired with a velocity $u = 50 \text{ ms}^{-1}$ from the ground at an angle $\theta$ with the horizontal. When the bullet is at its highest point of its trajectory,it collides head-on with the bob of the pendulum and gets embedded in the bob. After collision,if the pendulum moves through a maximum angle of $120^{\circ}$,then the value of $\theta$ is $(g = 10 \text{ ms}^{-2})$.

$A$ particle is moving in a circle of radius $r$ under the action of a force $F = \alpha r^2$ which is directed towards the centre of the circle. The total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy $= 0$ for $r = 0$).

$A$ motor engine pumps $1800 \,L$ of water per minute from a well of depth $30 \,m$ and allows it to pass through a pipe of cross-sectional area $30 \,cm^2$. Then the power of the engine is (Acceleration due to gravity,$g=10 \,m/s^2$) (in $\,kW$)

Given below are two statements:
Statement $I$: $A$ truck and a car moving with the same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance.
Statement $II$: $A$ car moving towards the east takes a turn and moves towards the north, the speed remains unchanged. The acceleration of the car is zero.
In the light of the given statements, choose the most appropriate answer from the options given below.

$A$ stationary object of mass $10 \ kg$ is subjected to two mutually perpendicular forces of $4 \ N$ and $3 \ N$. What will be its kinetic energy after $10 \ s$?