Given below are a few situations. Study them and state in which of the given cases work is said to be done. Give a reason for your answer:
$(i)$ $A$ person pushing hard a huge rock,but the rock does not move.
$(ii)$ $A$ bullock pulling a cart up to $1 \, km$ on the road.
$(iii)$ $A$ girl pulling a trolley for about $2 \, m$ distance.
$(iv)$ $A$ person standing with a heavy bag on his head.

(II, III) In physics,work is said to be done when a force applied on an object causes a displacement in the direction of the force. The formula is $W = F \times s \times \cos(\theta)$.
$(i)$ No work is done because the displacement $(s)$ is $0$,even though a force is applied.
$(ii)$ Work is done because the bullock applies force to the cart,resulting in a displacement of $1 \, km$.
$(iii)$ Work is done because the girl applies force to the trolley,resulting in a displacement of $2 \, m$.
$(iv)$ No work is done because the person is stationary,meaning the displacement $(s)$ is $0$.