$A$ crane pulls up a car weighing $500 \, kg$ to a vertical height of $4 \, m$. Calculate the work done by the crane. (in $J$)

State the law of conservation of energy.

$(i)$ Define power. Mention its $SI$ unit.
$(ii)$ $A$ boy of mass $50 \, kg$ runs up a staircase of $40$ steps in $8 \, s$. If the height of each step is $15 \, cm$,find his power. (Given,$g = 10 \, m \, s^{-2}$)

Define kinetic energy and potential energy. Write an expression for $KE$ of a body of mass $m$ moving with speed $v$. Find the kinetic energy of a stone of $10 \, kg$ moving with a velocity of $10 \, m s^{-1}$.

When a ball is lifted to a height of $h$ and then dropped,what is the kinetic energy of the ball just before it touches the ground?

$A$ man weighing $50 \, kg$ lifts a weight of $30 \, kg$ to the top of a building $10 \, m$ high. Find the work done by him. (Take $g = 9.8 \, m s^{-2}$) (in $, J$)