When a stone of mass $m$ falls through a vertical height $d$,the decrease in the gravitational potential energy is:

$A$ body is thrown vertically upwards. Its velocity goes on decreasing. What is the change in kinetic energy when its velocity becomes zero?

The velocity of a body moving in a straight line is increased by applying a constant force $F$, for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.

How much work is done by a weight lifter when he holds a weight of $80 \,kg$ on his shoulders for two minutes?

$A$ mass of $10 \, kg$ is dropped from a height of $50 \, cm$. Find its:
$(a)$ Potential energy just before dropping.
$(b)$ Kinetic energy just on touching the ground.
$(c)$ Velocity with which it hits the ground. (Given: $g = 10 \, m s^{-2}$)

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.