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?

Question

The mass of the space probe on planet Y will be greater than the mass 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 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 analyze the scenario, we need to distinguish between mass and weight:

• Mass is a measure of the amount of matter in an object and is unaffected by gravity. The mass of the space probes will be the same on both planets as they are identical.

• Weight is the force exerted on an object due to gravity and is calculated as the product of mass and gravitational acceleration (W = mg). The gravitational acceleration depends on the mass and radius of the planet.

Given that:

• Planet X has a mass (M_X) that is two times greater than the mass of Planet Y (M_Y).
• The gravity on each planet is determined by their mass and volume.

Since the volume of both planets is the same, the gravitational acceleration on each planet can be inferred from their respective masses.

• For Planet Y, we'll denote its mass as M. Therefore, for Planet X, M_X = 2M.
• The gravitational acceleration (g) on a planet is proportional to its mass and inversely proportional to the square of its radius.

Since both planets have the same volume, they must have different densities, which implies that Planet X will have a stronger gravitational pull due to its greater mass.

Therefore, the gravitational accelerations on the two planets will be:

• \( g_Y \) (for Planet Y) < \( g_X \) (for Planet X)

Now consider the probes:

• The mass of the space probes is the same on both planets (let's denote it as m).
• The weight (W) of the probes will be:
  • On Planet X: \( W_X = m \cdot g_X \)
  • On Planet Y: \( W_Y = m \cdot g_Y \)

Since \( g_X > g_Y \):

• \( W_X > W_Y \)

This leads us to the following conclusions based on your statements:

1. The mass of the space probe on planet Y will be greater than the mass of the space probe on planet X.

   • False (Mass is the same for both probes.)

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

   • False (Weight on X is greater.)

3. The mass of the space probe on planet X will be greater than the mass of the space probe on planet Y.

   • False (Again, mass is the same for both.)

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

   • True (Because \( g_X > g_Y \).)

Thus, the correct answer is: The weight of the space probe on planet X will be greater than the weight of the space probe on planet Y.