The weight of a person on a planet $A$ is about half that on the earth. He can jump up to $0.4 \, m$ height on the surface of the earth. How high can he jump on the planet $A$ (in $, m$)?

$(a)$ Give two conditions for work to be done.
$(b)$ What is the work done by frictional force on an object when dragged along a rough surface?
$(c)$ Relate power and work.
$(d)$ $A$ machine does $1960 \, J$ of work in $4 \, \text{minutes}$. What is the power?

In a tug-of-war,one team gives way to the other. What work is being done and by whom?

$A$ 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 $, J$)

$(i)$ An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the total work done against the force of gravity and by the force of gravity on the object? Explain with proper mathematical expression.
$(ii)$ $A$ certain force acting on a $20 \, kg$ mass changes its velocity from $5 \, m s^{-1}$ to $2 \, m s^{-1}$. Calculate the work done by the force.

$(i)$ 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,$g = 10 \, m \, s^{-2}$)