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 $, m$)?

Four men lift a $250 \,kg$ box to a height of $1 \,m$ and hold it without raising or lowering it. $(a)$ How much work is done by the men in lifting the box? $(b)$ How much work do they do in just holding it? $(c)$ Why do they get tired while holding it? $(g = 10 \,m \,s^{-2})$

$(a)$ Define power. Give its $SI$ unit.
$(b)$ Taking the example of a simple pendulum, explain the variations in the forms of energy and the interconversions involved.

$(a)$ What is meant by mechanical energy? State its two forms. State the law of conservation of energy. Give an example in which we observe a continuous change of one form of energy into another and vice-versa.
$(b)$ Calculate the amount of work required to stop a car of $1000 \, kg$ moving with a speed of $72 \, km \, h^{-1}$.

Justify giving proper reasoning whether the work done in the following case is positive or negative: Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.

$(i)$ Define the term potential energy. Write the $SI$ unit of potential energy.
$(ii)$ $A$ body of mass $50 \, kg$ is situated at a height of $10 \, m$. What is its potential energy? (Given $g = 10 \, m s^{-2}$)