If mass doubles while height remains constant, what happens to potential energy?

Potential energy is defined by the formula:

[ PE = mgh ]

where ( PE ) is the potential energy, ( m ) is the mass, ( g ) is the acceleration due to gravity, and ( h ) is the height above a reference point. In this formula, potential energy is directly proportional to mass. This means if the mass increases while the height and gravity remain constant, the potential energy will also increase in direct proportion to the mass.

When the question states that the mass doubles and the height stays the same, you can see that the new potential energy will be:

[ PE_{new} = (2m)gh = 2(mgh) = 2 \times PE_{original} ]

This clearly shows that doubling the mass leads to doubling the potential energy. The potential energy changes because there is more mass being acted on by gravity at the same height, resulting in an increase in energy stored due to the position of the object.

Thus, the potential energy doubles when the mass is doubled while keeping height constant.