AIIMS 2006 Physics Gravitation Assertion Reason Question

To analyze the question, we need to carefully evaluate both the Assertion and the Reason provided.

Assertion

A man in a closed cabin which is falling freely does not experience gravity.

This assertion is based on the principle of free fall and the concept of weightlessness. In a closed cabin that is in free fall, both the man and the cabin are accelerating downwards at the same rate due to gravity. According to the equivalence principle, the effects of gravity are indistinguishable from acceleration. Therefore, the man inside the cabin does not exert any force on the floor of the cabin, leading to the sensation of weightlessness.

Reason

Inertial and gravitational mass have equivalence.

This reason refers to a fundamental principle in physics known as the equivalence principle. It states that the inertial mass (the mass that resists acceleration) and gravitational mass (the mass that experiences gravitational attraction) are equivalent. This principle is a cornerstone of Einstein's General Theory of Relativity and explains why objects in free fall experience no net force acting on them, thus feeling weightless.

Evaluation of Options

1. Option A: Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

   • This option is incorrect because while both the Assertion and Reason are true, the Reason does not directly explain why the man does not experience gravity. The man feels weightless due to being in free fall, which is not solely explained by the equivalence of inertial and gravitational mass.

2. Option B: Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.

   • This is the correct answer. Both statements are true: the man does not feel gravity in free fall, and there is indeed an equivalence between inertial and gravitational mass. However, the reason does not directly explain the sensation of weightlessness experienced by the man, making this the correct choice.

3. Option C: Assertion is true, but Reason is false.

   • This option is incorrect because the Reason is true; inertial and gravitational mass are equivalent.

4. Option D: Both Assertion and Reason are false.

   • This option is incorrect as both statements are indeed true.

Conclusion

Thus, the correct answer is B, as both the Assertion and the Reason are true statements, but the Reason does not adequately explain the Assertion. The concept of free fall and the equivalence principle are related but do not imply that the equivalence principle alone explains the sensation of weightlessness experienced in a freely falling cabin.

Relevant Concepts

• Weightlessness in Free Fall: The sensation of weightlessness occurs because all objects in a freely falling system accelerate due to gravity at the same rate ($g \approx 9.81 \, \text{m/s}^2$).

• Equivalence Principle: This principle states that the laws of physics in a falling elevator (or cabin) are indistinguishable from those in free space, leading to the conclusion that locally (in small enough regions of spacetime), inertial effects and gravitational effects cannot be told apart.

In summary, understanding the nuances of these principles helps clarify why the correct answer is B, emphasizing the nature of free fall and the equivalence of mass.