Inverse Square Law and Gravitational Forces

Two new planets are discovered, planet X and planet Y. The planets have identical volumes, but the mass of planet X is two times greater than the mass of planet Y. If two identical space ships land on each planet, which of the following will be true?

• The mass of the space ship on planet Y will be greater than the mass of the space ship on planet X.

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

• The mass of the space ship on planet X will be greater than the mass of the space ship on planet Y.

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

Answer explanation

Weight is the force due to gravity, which depends on mass and gravitational acceleration. Since planet X has greater mass, the weight of the space ship on planet X will be greater than on planet Y.

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NGSS.MS-PS2-4

If Earth had twice the mass it has now, how would the gravitational force between

• The gravitational force would be twice as much as it is now.

• The gravitational force would be four times as much as it is now.

• The gravitational force would be half as much as it is now.

• The gravitational force would be the same as it is now.

Answer explanation

The gravitational force is directly proportional to mass. If Earth had twice the mass, the gravitational force would also be twice as much as it is now, making the correct choice: 'The gravitational force would be twice as much as it is now.'

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• Earth, Mars, Venus

• Earth, Venus, Mars

• Venus, Mars, Earth

• Venus, Earth, Mars

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Which of the diagrams shows the greatest gravitational force?

• I

• II

• III

• IV

Answer explanation

Diagram II shows the greatest gravitational force because it likely represents the closest proximity of masses, which increases gravitational attraction according to Newton's law of universal gravitation.

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NGSS.MS-PS2-4

Which of the diagrams shows the least gravitational force?

• I

• II

• III

• IV

Answer explanation

Diagram IV shows the least gravitational force because it likely represents the greatest distance between the masses or the smallest mass, both of which reduce gravitational attraction according to Newton's law of gravitation.

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• The diameters of the objects in Figure A are greater than the diameters of the objects in Figure B.

• The masses of the objects in Figure A are less than the mass of the objects in Figure B.

• The distance between the objects in Figure A is shorter than the distance between the objects in Figure B.

• The surface area of the larger object in Figure A is greater than the surface area of the larger object in Figure B.

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NGSS.MS-PS2-4

Which of the following graphs best represents the gravitational force between two point masses as a function of the distance between the masses?

• 
• 
• 
• 

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As mass decreases, gravitational force does what?

• Increases

• Decreases 

• Remains the same

• Changes

Answer explanation

As mass decreases, the gravitational force also decreases, according to the formula F = G(m1*m2)/r^2. Thus, the correct answer is 'Decreases'.

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Which of the following is Newton's Law on Gravitation?

• F=Gm₁m₂/r

• F = Gm₁m₂/r²

• F = Gm₁m₂/2r

• F = m₁m₂/2r

Answer explanation

Newton's Law of Gravitation states that the force (F) between two masses (m1 and m2) is proportional to the product of their masses and inversely proportional to the square of the distance (r) between them, expressed as F = Gm1m2/r².

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Two factors effecting the magnitude of the force of gravity between 2 objects are...

• mass and distance 

• mass and matter

• distance and weight 

• weight and mass

Answer explanation

The force of gravity between two objects is determined by their mass and the distance between them. Greater mass increases gravitational force, while greater distance decreases it, making 'mass and distance' the correct choice.

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