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

options:

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

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 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.

Answer 1

To solve the problem, we need to understand the relationship between mass, weight, and the gravitational force exerted by each planet.

1. Weight of an object is given by the formula: \[ \text{Weight} = m \cdot g \] where \( m \) is the mass of the object and \( g \) is the acceleration due to gravity on the planet.

2. Gravitational acceleration \( g \) on a planet can be calculated using the formula: \[ g = \frac{G \cdot M}{R^2} \] where \( G \) is the gravitational constant, \( M \) is the mass of the planet, and \( R \) is the radius of the planet. Since both planets have identical volumes, they will have similar radii if they have the same density.

Let’s denote the mass of planet Y as \( m_Y \) and the mass of planet X as \( m_X = 2 \cdot m_Y \). Since the planets have the same volume, their densities and thus gravitational accelerations will differ due to their mass differences.

3. Since the volume \( V \) is the same for both planets, we can express density \( \rho \) as: \[ \rho = \frac{m}{V} \] Hence:

   • For Planet Y: \( \rho_Y = \frac{m_Y}{V} \)
   • For Planet X: \( \rho_X = \frac{m_X}{V} = \frac{2 \cdot m_Y}{V} = 2 \cdot \rho_Y \)

4. The gravitational acceleration for each planet can thus be inferred:

   • Planet Y: \( g_Y = k \cdot m_Y \) (some constant based on the volume and radius)
   • Planet X: \( g_X = k \cdot (2 \cdot m_Y) = 2 \cdot g_Y \)

5. Weight of the probes:

   • Let the mass of the space probe be \( m_p \).
   • On Planet Y: \[ \text{Weight}_Y = m_p \cdot g_Y \]
   • On Planet X: \[ \text{Weight}_X = m_p \cdot g_X = m_p \cdot (2 \cdot g_Y) = 2 \cdot (m_p \cdot g_Y) = 2 \cdot \text{Weight}_Y \]

From this analysis:

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

6. The mass of the space probe will remain constant regardless of which planet it is on. Hence:

• The mass of the space probe is the same on both planets.

Summary of conclusions:

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

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.

Answer 2

Which statement best describes the gravitational force between objects?

options:

Objects exert a gravitational force only on objects close to them.
Objects exert a gravitational force only on objects close to them.

Only large massed objects exert gravitational force on every other object.
Only large massed objects exert gravitational force on every other object.

Objects exert a gravitational force on every other object.
Objects exert a gravitational force on every other object.

Only large massed objects exert gravitational force on objects close to them.

Answer 3

The statement that best describes the gravitational force between objects is:

Objects exert a gravitational force on every other object.

This statement is true because, according to the law of universal gravitation, every mass attracts every other mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This means that even small objects exert gravitational forces on one another, although these forces may be very weak compared to those exerted by larger masses (such as planets and stars). Hence, all objects, regardless of their size, exert gravitational forces on all other objects.