$A$ 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 $\,kW$)

Two balls $A$ and $B$ having masses $1\, kg$ and $2\, kg$,moving with speeds $21\, m/s$ and $4\, m/s$ respectively in opposite directions,collide head-on. After the collision,$A$ moves with a speed of $1\, m/s$ in the same direction. Which of the following statements is correct?

$A$ person trying to lose weight (dieter) lifts a $10\; kg$ mass,one thousand times,to a height of $0.5\; m$ each time. Assume that the potential energy lost each time she lowers the mass is dissipated.
$(a)$ How much work does she do against the gravitational force?
$(b)$ Fat supplies $3.8 \times 10^{7} \;J$ of energy per kilogram which is converted to mechanical energy with a $20\%$ efficiency rate. How much fat will the dieter use up?

$A$ bullet of mass $0.02 \ kg$ travelling horizontally with velocity $250 \ ms^{-1}$ strikes a block of wood of mass $0.23 \ kg$ which rests on a rough horizontal surface. After the impact,the block and bullet move together and come to rest after travelling a distance of $40 \ m$. The coefficient of sliding friction of the rough surface is $\left(g=9.8 \ ms^{-2}\right)$

$A$ sphere of mass $m$,moving with velocity $V$,enters a hanging bag of sand and stops. If the mass of the bag is $M$ and it is raised by height $h$,then the velocity of the sphere was

Which of the following graphs correctly represents the relationship between kinetic energy $(E)$,potential energy $(U)$,and height $(h)$ from the ground for a particle moving vertically?