To determine the relationship between the mass and weight of the space probes on the two planets, we need to consider the following points:
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Mass: The mass of an object does not change regardless of its location in the universe. Therefore, if the space probes are identical and have the same mass, the mass of the space probe on planet X and the mass of the space probe on planet Y will be the same.
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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 of the planet it is on. The formula for weight \( W \) is given by:
\[ W = m \cdot g \]
where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity on the respective planet.
Since planet X has a mass that is twice that of planet Y, the gravitational acceleration \( g \) on planet X will be greater than that on planet Y (assuming equal volumes and that the densities are different enough to account for the mass difference). This means that the weight of the space probe on planet X will be greater than the weight of the space probe on planet Y.
Therefore, the correct statement is:
The weight of the space probe on planet X will be greater than the weight of the space probe on planet Y.