Two balls, A and B have the same gravitational potential energy. Ball A is six times the mass of ball B. How do their heights above the ground compare?

Height of A is one-sixth the height of B.

Reason — The gravitational potential energy of a body of mass m raised to a height h is U = mgh.

Given,

m_A = 6m_B and U_A = U_B

So,

$$\begin{aligned}\text m_\text A \text g \text h_\text A = \text m_\text B \text g \text h_\text B \\[1em] \Rightarrow 6\text m_\text B \text g \text h_\text A = \text m_\text B \text g \text h_\text B \\[1em] \Rightarrow \text h_\text A = \frac{\text h_\text B}{6}\end{aligned}$$

Hence, the height of A is one-sixth the height of B.