Understanding Amount of Matter and Weight

The question asks about the amount of matter in the same weight at different locations like the North Pole, the Equator, and the Moon. To answer this, we need to understand the difference between mass (amount of matter) and weight.

• Mass: Mass is the fundamental property of an object that measures the amount of matter it contains. It is an intrinsic property and does not change with location, temperature, pressure, or the presence of gravitational fields. It is typically measured in kilograms (kg).
• Weight: Weight is the force exerted on an object due to gravity. It is calculated using the formula: \( W = m \times g \), where \( W \) is weight, \( m \) is mass, and \( g \) is the acceleration due to gravity at that location. Weight is a force and is measured in Newtons (N).

The acceleration due to gravity \( g \) is not the same at all locations:

• On Earth, \( g \) is slightly higher at the poles than at the equator due to the Earth's shape and rotation.
• On the Moon, \( g \) is significantly lower, approximately one-sixth of the value on Earth.

Since weight depends on gravity ($W = mg$), the weight of an object changes with location even though its mass remains constant.

The question asks about the "amount of matter" (mass) when the "weight" is the same. Let's consider an object with a specific weight, say \( W_0 \). The mass of this object at a location with gravity \( g \) would be \( m = \frac{W_0}{g} \). If we interpret "same weight" to mean a fixed numerical value for weight, then the mass required to achieve that weight would vary with \( g \). For example:

• At the North Pole (high \( g \)), the mass would be relatively low ($m_{pole} = W_0 / g_{pole}$).
• At the Equator (lower \( g \)), the mass would be relatively higher ($m_{equator} = W_0 / g_{equator}$).
• On the Moon (very low \( g \)), the mass would be much higher ($m_{moon} = W_0 / g_{moon}$).

However, the fundamental definition of the amount of matter (mass) is that it is an intrinsic property of the object itself, regardless of its location or the gravitational force acting upon it. The question is likely testing this core concept.

Even though the force of gravity (which determines weight) changes with location, the inherent amount of substance or matter in an object remains constant. Therefore, if we are considering the fundamental property of the amount of matter, it is the same regardless of whether the object is at the North Pole, the Equator, or the Moon.

The amount of matter, which is mass, does not change with location. An object with a certain mass on Earth has the same mass on the Moon or anywhere else in the universe. While its weight changes due to varying gravity, the quantity of matter composing it stays the same.

Hence, the amount of matter in an object is the same at all of the mentioned places.