Understanding Weightlessness and Inertia

The question asks about the properties of bodies when they are in a weightless state. To answer this, we need to understand what weight and inertia are and how they are affected by the state of weightlessness.

What is Weight?

Weight is the force exerted on a body due to gravity. It is calculated using the formula:

\(W = mg\)

where \(m\) is the mass of the body and \(g\) is the acceleration due to gravity. In a state of weightlessness, the effect of gravity is essentially zero or appears to be zero (for example, in freefall or in orbit). This means the value of \(g\) relevant to measuring weight becomes zero. Therefore, in a weightless state, the weight (\(W\)) of the body is zero.

What is Inertia?

Inertia is the property of a body by which it resists any change in its state of motion (whether at rest or in motion). Inertia is a fundamental property of matter and is directly related to the mass of the body. A more massive object has greater inertia, meaning it is harder to start moving if it is at rest, or harder to stop or change direction if it is in motion.

Mass is an intrinsic property of a body; it represents the amount of matter contained in it. Unlike weight, mass does not depend on gravity or the location of the body. It remains constant whether the body is on Earth, the Moon, or in space.

Bodies in a Weightless State

When a body is in a weightless state:

• The force of gravity acting on it is negligible or zero, so its weight is zero.
• Its mass, which is an intrinsic property, remains unchanged.
• Since inertia is directly related to mass, the body still possesses its full inertia.

Even though a body has no weight in a weightless state, it still has mass, and you would still need to apply a force to accelerate it or change its direction due to its inertia. For instance, an astronaut in space (weightless) pushing a large object would still find it hard to move because of its inertia (large mass), even though the object has no weight.

Analyzing the Options

Let's look at the given options based on our understanding:

• Option 1: "have no weight, no inertia" - This is incorrect because bodies always possess inertia due to their mass.
• Option 2: "have weight, have inertia" - This is incorrect because in a weightless state, bodies have no weight, although they do have inertia.
• Option 3: "have no weight, but possess inertia" - This aligns with our understanding that weight is zero in a weightless state, but mass (and thus inertia) is still present.
• Option 4: "have weight, but don’t possess inertia" - This is incorrect because bodies in a weightless state have no weight and always possess inertia due to their mass.

Therefore, in the weightless state, bodies have no weight but still possess inertia.