State whether the following statement is true or false:
Work done by centripetal force is zero.

How much work should be done on an object of $120 \, kg$ to increase its speed from $25 \, m s^{-1}$ to $40 \, m s^{-1}$ (in $, J$)?

Can any object have mechanical energy even if its momentum is zero? Explain.

An object of mass $40 \text{ kg}$ is pulled up to a height of $0.5 \text{ m}$. Calculate the work done. (Given $g = 9.8 \text{ m s}^{-2}$) (in $J$)

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

How is the power related to the speed at which a body can be lifted? How many kilograms will a man working at the power of $100\, W$ be able to lift at a constant speed of $1\, m\, s^{-1}$ vertically (in $, kg$)? $(g = 10\, m\, s^{-2})$