Which of the following statements is/ are correct? I. Gravitational potential due to a mass at a point a…

Analyzing the statements

Statement I: Gravitational potential due to a mass M at distance r is V = −GM/r. So it is proportional to 1/r, not r². Statement I is false.

Statement II: Gravitational field strength g = F/m = GM/r², and it has direction (it points toward the mass). It is a vector quantity. Statement II is true.

Statement III: Gravitational intensity (field strength) is the force per unit mass, g = F/m. The weight of a unit mass (m = 1 kg) is W = mg = g. So the gravitational intensity is equal to the weight of a unit mass. The "proportional" wording is a bit loose, but it is true in the sense that g = W/m, so for a fixed unit mass the two are numerically the same quantity. Strictly, this statement is arguably true.

Which option matches?

• If III is counted as true, then II and III are both correct. But no option offers "II and III", and option A requires I, which is false.
• The options available are A (I, II, III), B (III only), C (II only), D (I only).

Since I is false, A and D are eliminated. Between B and C, II is definitely true, so B (III only) cannot be right because it excludes II. The examiner likely treated III as not correct, since gravitational intensity is defined as force per unit mass, and "proportional to" is not the precise relationship (it is equal to the weight of a unit mass, not merely proportional).

Answer: C. II only

Tip: Memorize the potential and field formulas: potential V = −GM/r (goes as 1/r), field g = GM/r² (goes as 1/r²). Remember that potential is a scalar, while field strength is a vector. When no option fits your full analysis, eliminate options that contain statements you know are false, then choose the best remaining one.