$A$ person continues to push a heavy mass for some time but fails to move it. What is the work done by him?

$(a)$ The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?
$(b)$ An object is dropped from a height $h$. When is its
$(i)$ potential energy maximum?
$(ii)$ kinetic energy maximum?

$A$ light and a heavy body have the same momentum. Which one will have greater kinetic energy?

$(a)$ How much work is done when a force of $1\, N$ moves a body through a distance of $1\, m$ in its direction?
$(b)$ Is it possible that a force is acting on a body but still the work done is zero? Explain giving one example.

Two children $A$ and $B$ each weighing $20 \, kg$ climb a rope up to a height of $10 \, m$. Child $A$ takes $10 \, s$ and child $B$ takes $20 \, s$ to climb. State whether the work done by both is equal or unequal. Who has more power?

$A$ $2 \, m$ 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 $, J$)?