An object of mass $1 \, kg$ has a potential energy of $1 \, J$ relative to the ground when it is at a height of: (in $, m$)

State whether the following statement is true or false:
Work and energy have different units.

$(a)$ $A$ person is holding a bucket of water by applying a vertical force of $100 \, N$. He first moves a horizontal distance of $5 \, m$ and then climbs up through stairs a vertical distance of $10 \, m$. Calculate the total work done by the person on the bucket.
$(b)$ Establish the relationship between kinetic energy and momentum of a body.

Seema tried to push a heavy rock of $100 \, kg$ for $200 \, s$ but could not move it. Find the work done by Seema at the end of $200 \, s$. (in $, J$)

The work done in lifting a box onto a platform does not depend upon how fast it is lifted up. Explain your answer giving proper reasoning.

$(a)$ How much work is done when a force of $1\, N$ moves a body through a distance of $1\, m$ in its direction?
$(b)$ Is it possible that a force is acting on a body but still the work done is zero? Explain giving one example.