An object is placed on a shelf 2 m above the ground. If the shelf is raised to 4 m, what happens to the potential energy of the object?

The correct option is: The potential energy doubles.

To understand why this is correct, we can look at the formula for gravitational potential energy ($PE$):

$PE=m·g·h$

where:
- $m$ is the mass of the object,
- $g$ is the acceleration due to gravity, and
- $h$ is the height of the object above the ground.

Initially, the object is placed at a height of $h_1=2\text{m}$. Its initial potential energy ($P{E}_1$) is:

$P{E}_1=m·g·2$

When the shelf is raised to $h_2=4\text{m}$, the new potential energy ($P{E}_2$) becomes:

$P{E}_2=m·g·4$

By comparing the new potential energy to the initial potential energy, we get:

$P{E}_2=m·g·(2·2)=2·(m·g·2)=2·P{E}_1$

Since the height doubles from 2 m to 4 m, and potential energy is directly proportional to the height, the potential energy of the object also doubles.