Question

Scientists discovered two new planets: planet X and planet Y. They have identical volumes, but the mass of planet X is two times greater than the mass of planet Y. If two identical space probes land on each planet, which of the following will be true?(1 point) Responses The weight of the space probe on planet Y will be greater than the weight of the space probe on planet X. The weight of the space probe on planet Y will be greater than the weight of the space probe on planet X. The mass of the space probe on planet Y will be greater than the mass of the space probe on planet X. The mass of the space probe on planet Y will be greater than the mass of the space probe on planet X. The mass of the space probe on planet X will be greater than the mass of the space probe on planet Y. The mass of the space probe on planet X will be greater than the mass of the space probe on planet Y. The weight of the space probe on planet X will be greater than the weight of the space probe on planet Y.

Answer 1

To determine the correct statements regarding the weights and masses of the space probes on planets X and Y, we can analyze the information provided:

1. Mass of the Planets:

   • Let the mass of planet Y be \( M \).
   • Therefore, the mass of planet X is \( 2M \).

2. Volume:

   • Both planets have identical volumes.

3. Weight of an Object:

   • The weight \( W \) of an object (like the space probe) is given by the equation: \[ W = m \cdot g \]
   • Where \( m \) is the mass of the object and \( g \) is the gravitational acceleration on that planet.

4. Gravitational Acceleration:

   • The gravitational acceleration \( g \) on a planet can be determined by: \[ g \propto \frac{M}{r^2} \]
   • Since both planets have the same volume, we can assume they have the same radius (as \( r \) is proportional to volume in this case).

5. Calculating \( g \):

   • For Planet Y with mass \( M \): \[ g_Y \propto \frac{M}{r^2} \]
   • For Planet X with mass \( 2M \): \[ g_X \propto \frac{2M}{r^2} = 2 \cdot g_Y \]

This means the gravitational acceleration on planet X is twice that of planet Y.

6. Weight of the Probes:
   • Since the probes have the same mass (let's say \( m \)):
     • Weight of the probe on planet X: \[ W_X = m \cdot g_X = m \cdot 2g_Y \]
     • Weight of the probe on planet Y: \[ W_Y = m \cdot g_Y \]

Now, comparing the weights: \[ W_X = 2 \cdot W_Y \quad (\text{because } g_X = 2g_Y) \]

This means the weight of the space probe on planet X will be greater than the weight of the space probe on planet Y.

7. Mass of the Probes:
   • The mass of the probes does not change based on the gravitational environment; thus, the mass of the space probe on both planets will be the same:
     • Mass on planet X = Mass on planet Y = \( m \).

Conclusion:

• The weight of the space probe on planet X will be greater than the weight of the space probe on planet Y.
• The mass of the space probe will be the same on both planets.

The correct choice is:

• The weight of the space probe on planet X will be greater than the weight of the space probe on planet Y.