Question

Each pair of clay balls represents two planetesimals. If each planetesimal is composed of the same material and is separated by the same
distance, which pair experiences the greatest gravitational attraction?

Answer 1

The pair in the top right corner is the one which experiences the greatest gravitational attraction.

Explanation:

The magnitude of the gravitational force between two objects is given by  the equation:

$F=G\frac{m_1 m_2}{r^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

$m_1,m_2$ are the masses of the two objects

r is the separation between them

In this problem, we are comparing the gravitational force between the 4 pairs of planetesimals. First of all, we notice that all the 4 pairs have same  distance r, therefore we can neglect this factor in our calculation.

Then, we observe that the magnitude of the gravitational force is proportional to the product between the masses:

$F\propto m_1 m_2$

this means that the pair with the largest gravitational force is the one with the largest product of the two masses. By looking at the picture, we see that the pair with the largest planetesimals is the pair in the top right corner; and since all the planetesimals have the same density (because they are made from the same material), this means that the pair in the top right corner is the one which experiences the greatest gravitational attraction.

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Answer 2

From the picture, of all the pairs of clay balls that represent two planetesimals, the one on the top right will experience the greatest gravitational attraction.    

The gravitational force is given by:

$F = \frac{GmM}{r^{2}}$   (1)

Where:

• G is the gravitational constant = 6.67x10⁻¹¹ N*m²*kg⁻²

• m and M are the masses of the first and second balls

• r is the distance between the planetesimals    

   

From equation (1), we can see that the gravitational force is directly proportional to the masses of the planetesimals and inversely proportional to the distance. The pair of planetesimals with bigger balls (more mass) will have the greatest gravitational attraction since the distance is the same for each of them.          

 

In the picture, of all the planetesimals, the second one (top right) will have the greatest gravitational attraction since its pair of balls are the largest (bigger product m*M). On the contrary, the pair of balls on the down left will have the lowest gravitational attraction (they are the smallest).                        

                 

Therefore, the pair of balls on the top right will experience the greatest gravitational attraction.    

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I hope it helps you!