What is the total gravitational potential energy of this system of masses?

• A. $-1.52\times 10^{-9}$ J
• B. $-3.49\times 10^{-8}$ J
• C. $-7.78\times 10^{-8}$  J
• D. $-1.75\times 10^{-7}$ J

Answer: (D)

Verified step by step guidance

1. Identify the masses involved in the system: 20 kg, 10 kg, and 30 kg. Note their positions relative to each other as shown in the image.
2. Understand that gravitational potential energy between two masses is given by the formula: $-\frac{Gmmmm}{r}$, where $G$ is the gravitational constant, $m$ and $m$ are the masses, and $r$ is the distance between them.
3. Calculate the gravitational potential energy between each pair of masses: (20 kg and 10 kg), (20 kg and 30 kg), and (10 kg and 30 kg). Use the distances provided in the image: 30 cm between 20 kg and 10 kg, and 40 cm between 20 kg and 30 kg.
4. Convert the distances from centimeters to meters for consistency in units, as the gravitational constant $G$ is typically used in meters.
5. Sum the gravitational potential energies calculated for each pair to find the total gravitational potential energy of the system.