WAEC Physics 2011 Paper

Concept:The acceleration due to gravity $g$ is the gravitational force experienced per unit mass at a distance $R$ from the centre of mass $M$.Explanation:Consider a test mass $m$ placed at a distance $R$ from the centre of mass $M$.By Newton's law of gravitation, the attractive force is:$$F = \frac{GMm}{R^2}$$According to Newton's second law, this force equals the weight of the mass:$$F = mg$$Equating the two expressions gives:$$mg = \frac{GMm}{R^2}$$Cancelling $m$ on both sides yields the required relationship:$$g = \frac{GM}{R^2}$$This matches option B.Answer:Option B: $g = \frac{GM}{R^2}$