Consider the following statements: I. The weight of an object is the same everywhere on the surface of the Earth, but its inertial mass could be different. II. The inertial mass and gravitational mass of an object are proportional and the proportionality constant is the same everywhere. III. The inertial mass and weight of an object are the same at different places on Earth. Which of the statements given above is/are correct?
II only
Statement I is incorrect: the weight of an object (\(W = mg\)) is not the same everywhere on the Earth's surface because the acceleration due to gravity g varies slightly with latitude and altitude, while the inertial mass of the object stays constant everywhere. Statement II is correct: inertial mass and gravitational mass are always directly proportional, and with a consistent choice of units this proportionality constant is taken as 1 and remains the same at every location -- this is the basis of the equivalence principle. Statement III is incorrect: although inertial mass stays the same everywhere, weight changes from place to place as g changes, so inertial mass and weight are not both "the same at different places". Hence only statement II is correct.
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