Energy comparison – potential energy of a raised body vs. kinetic energy of a falling body\nFor the same mass and height reference, the potential energy of a vertically raised body is ______ the kinetic energy gained by a body after freely falling through that height (neglect air resistance).

Introduction / Context:
This question examines conservation of mechanical energy for vertical motion under gravity. When air resistance is negligible, potential energy (PE) and kinetic energy (KE) interconvert.

Given Data / Assumptions:

• Mass m is the same in both comparisons.
• Height h is the same (reference taken from the lower level).
• Gravitational acceleration g is constant; air resistance is neglected.

Concept / Approach:
Potential energy at height h is PE = m g h. If a body falls freely from rest through height h, its loss in potential energy equals its gain in kinetic energy by energy conservation, so KE at the lower level becomes m g h.

Step-by-Step Solution:

Verification / Alternative check:
Use kinematics: v^2 = u^2 + 2 g h with u = 0 ⇒ v^2 = 2 g h ⇒ KE = 0.5 m v^2 = 0.5 m (2 g h) = m g h, agreeing with energy conservation.

Why Other Options Are Wrong:

• Less than / greater than: contradict conservation of mechanical energy for ideal free fall.
• Cannot be compared: sufficient information is provided under standard assumptions.

Common Pitfalls:
Forgetting to neglect air resistance; with drag, some energy is dissipated as heat and sound, so KE would be less than m g h.

Final Answer:
equal to