To determine the correct statements regarding the space probes on planets X and Y, let's analyze the situation based on gravitational effects.
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Weight: The weight of an object is given by the formula \( W = m \cdot g \), where \( m \) is the mass of the object and \( g \) is the gravitational acceleration on the surface of the planet. Since the two planets have identical volumes but different masses, the gravitational acceleration will differ between them.
- Let the mass of planet Y be \( m \) and the mass of planet X be \( 2m \).
- The gravitational attraction (and thus the surface gravity, \( g \)) is proportional to the mass of the planet and inversely proportional to the square of its radius. Since both planets have the same volume, we can infer that:
- Planet X, being more massive, will have a greater surface gravity \( g_X \) than planet Y \( g_Y \). Thus, \( g_X > g_Y \).
- 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 because \( W_X = m_{probe} \cdot g_X > W_Y = m_{probe} \cdot g_Y \).
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Mass: The mass of the space probes does not change based on the gravitational field of the planets they land on. The mass of space probes is a property of the probes themselves and remains constant regardless of the planet. Therefore:
- The mass of the space probes on planet X is equal to the mass of the space probes on planet Y.
Now, we can analyze the responses:
- The weight of the space probe on planet X will be greater than the weight of the space probe on planet Y. (True)
- The mass of the space probe on planet Y will be greater than the mass of the space probe on planet X. (False)
- The weight of the space probe on planet Y will be greater than the weight of the space probe on planet X. (False)
- The mass of the space probe on planet X will be greater than the mass of the space probe on planet Y. (False)
The correct response is: The weight of the space probe on planet X will be greater than the weight of the space probe on planet Y.