$A$ $2 \, m$ high person is holding a $25 \, kg$ trunk on his head and is standing at a roadways bus-terminus. How much work is done by the person (in $, J$)?

$(a)$ Define potential energy. Write an expression for potential energy of an object of mass $m$ raised through a height $h$.
$(b)$ Find the energy possessed by an object of mass $10 \, kg$ when it is raised to a height of $6 \, m$ above the ground. (Given $g = 9.8 \, m s^{-2}$)

State whether the following statement is true or false:
Work done by centripetal force is zero.

$(i)$ $A$ light and a heavy object have the same momentum. What is the ratio of their kinetic energies? Which one has a larger kinetic energy?
$(ii)$ $A$ ball is dropped from a height of $10\, m$. If the energy of the ball reduces by $40\%$ after striking the ground,how high can the ball bounce back? $(g = 10\, m s^{-2})$

$A$ person is holding a bucket by applying a vertical force of $10 \,N$. He moves a horizontal distance of $5 \,m$ and then climbs up a vertical distance of $10 \,m$. Calculate the total work done by him. (in $J$)

$A$ boy of mass $40 \, kg$ runs up a flight of $50$ steps,each $10 \, cm$ high,in $5 \, s$. Find: $(i)$ the work done by the boy,and $(ii)$ the power developed. $(g = 9.8 \, m s^{-2})$