To analyze the situation, we need to understand the difference between mass and weight, particularly how they relate to the planets in question.
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Mass: The mass of the space probe is a property of the probe itself and does not change depending on the location. Thus, the mass of the space probe is the same regardless of whether it is on planet X or planet Y.
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Weight: Weight is the force exerted on an object due to gravity, which depends on both the mass of the object and the gravitational acceleration at that location. The weight of the space probe on each planet can be calculated using the formula: \[ \text{Weight} = \text{mass} \times \text{gravity} \]
Since the two planets have identical volumes but different masses, we can determine their gravitational accelerations. Given that the mass of planet X is twice that of planet Y, it follows that the gravitational force (acceleration due to gravity) on planet X will be greater than on planet Y, assuming uniform density (since gravity on a planet is directly proportional to its mass).
Let’s denote:
- Mass of planet Y = \( M \)
- Mass of planet X = \( 2M \)
Now, considering volume is the same for both planets, their densities (mass/volume) will differ. Planet X will have a higher density than planet Y, and hence a stronger gravitational pull on its surface.
As a result:
- The weight of the space probe on planet X will be greater than the weight of the space probe on planet Y.
Therefore, among the options provided:
- The weight of the space probe on planet X will be greater than the weight of the space probe on planet Y is the true statement.
Thus, the correct assertion is:
- The weight of the space probe on planet X will be greater than the weight of the space probe on planet Y.
2 answers