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Question 4 of 10

The table below shows the acceleration of gravity on different bodies in the solar system.

\begin{tabular}{|c|c|}
\hline
Object & \begin{tabular}{c}
Acceleration of Gravity \\
[tex]$\left( m / s ^2\right)$[/tex]
\end{tabular} \\
\hline
Earth & 9.8 \\
Mercury & 3.59 \\
Mars & 3.7 \\
Neptune & 14.07 \\
Uranus & 9.0 \\
Pluto & 0.42 \\
\hline
\end{tabular}

On which body would a 30 kg bowling ball have the least gravitational potential energy when lifted to a height of 1 m?

A. Mars
B. Earth
C. Uranus
D. Mercury



Answer :

To determine on which body a 30 kg bowling ball would have the least gravitational potential energy when lifted to a height of 1 meter, we need to calculate the gravitational potential energy for each body. The formula for gravitational potential energy ([tex]\(E_p\)[/tex]) is:

[tex]\[ E_p = m \cdot g \cdot h \][/tex]

where:
- [tex]\( m \)[/tex] is the mass of the object (30 kg),
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height (1 meter).

Given the acceleration of gravity for each body:
- Earth: [tex]\( g = 9.8 \, m/s^2 \)[/tex]
- Mercury: [tex]\( g = 3.59 \, m/s^2 \)[/tex]
- Mars: [tex]\( g = 3.7 \, m/s^2 \)[/tex]
- Neptune: [tex]\( g = 14.07 \, m/s^2 \)[/tex]
- Uranus: [tex]\( g = 9.0 \, m/s^2 \)[/tex]
- Pluto: [tex]\( g = 0.42 \, m/s^2 \)[/tex]

Now, let’s calculate the gravitational potential energy for each body.

1. Earth:
[tex]\[ E_p = 30 \, kg \times 9.8 \, m/s^2 \times 1 \, m = 294.0 \, J \][/tex]

2. Mercury:
[tex]\[ E_p = 30 \, kg \times 3.59 \, m/s^2 \times 1 \, m = 107.7 \, J \][/tex]

3. Mars:
[tex]\[ E_p = 30 \, kg \times 3.7 \, m/s^2 \times 1 \, m = 111.0 \, J \][/tex]

4. Neptune:
[tex]\[ E_p = 30 \, kg \times 14.07 \, m/s^2 \times 1 \, m = 422.1 \, J \][/tex]

5. Uranus:
[tex]\[ E_p = 30 \, kg \times 9.0 \, m/s^2 \times 1 \, m = 270.0 \, J \][/tex]

6. Pluto:
[tex]\[ E_p = 30 \, kg \times 0.42 \, m/s^2 \times 1 \, m = 12.6 \, J \][/tex]

Now we compare the gravitational potential energies:

- Earth: 294.0 J
- Mercury: 107.7 J
- Mars: 111.0 J
- Neptune: 422.1 J
- Uranus: 270.0 J
- Pluto: 12.6 J

From these calculations, we see that the least gravitational potential energy is on Pluto with [tex]\( 12.6 \, J \)[/tex]. Therefore, the 30 kg bowling ball would have the least gravitational potential energy on Pluto when lifted to a height of 1 meter.

The correct answer is:
- Pluto