How does the work needed to lift an object and the gravitational potential energy of the object compare?
they are equal.
the work is greater.
the work is less.
the comparison depends on the height.

They are equal.

Explanation:

For the law of conservation of energy, the work done when lifting an object by a heigh is equal to the gravitational potential energy gained by the object.

In fact:

- the work done when lifting the object is equal to the force applied times the displacement:

(1)

however, when the object is lifted at constant speed, the force applied is equal to the weight of the object, mg, while the displacement is equal to the change in height, . So, (1) becomes

But the gain in gravitational potential energy of the object is

So, we see that this is equal to the work done.