The potential energy (PE) of an object at height \( h \) is given by the formula:
\[ PE = mgh \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (which is constant near the Earth's surface), and
- \( h \) is the height above a reference point.
In this scenario, we have:
- Mass of rock A: \( m_A = 2m_B \) (rock A's mass is twice that of rock B)
- Mass of rock B: \( m_B \)
- Both rocks are at the same height \( h \).
Now we can express the potential energies of rocks A and B.
For rock A: \[ PE_A = m_A \cdot g \cdot h = (2m_B) \cdot g \cdot h = 2m_Bgh \]
For rock B: \[ PE_B = m_B \cdot g \cdot h = m_Bgh \]
Now let’s compare the potential energies:
\[ PE_B = m_Bgh \] \[ PE_A = 2m_Bgh \]
This shows that:
\[ PE_A = 2 \cdot PE_B \]
Thus, rock B has half the potential energy of rock A:
\[ PE_B = \frac{1}{2} PE_A \]
So the answer is:
C. Rock B has one-half the potential energy of rock A.