Question

Surface gravity of different planets in correct decreasing order is
A. Neptune, Jupiter, Saturn, Earth
B. Jupiter, Neptune, Earth, Saturn
C. Jupiter, Neptune, Saturn, Earth
D. Jupiter, Uranus, Neptune, Saturn

Answer 1

Hint: When two bodies are in the vicinity of each other force of gravity acts between then. The formula for calculating the magnitude of this gravity is given below. If one of the masses is immensely large compared to the other body, as in case of planets and real objects on the planets, then the mass and size of the lighter body can be ignored. So, in case of planets, the gravitational force on surface or surface gravity is given by the formula given below. And the data for each planet is known to us.

Formula used:
\[F=\dfrac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\]
\[F=\dfrac{Gm}{{{r}^{2}}}\]

Complete step-by-step answer:
Gravitational force between two bodies is given by
\[F=\dfrac{G{{m}_{1}}{{m}_{2}}}{{{r}^{2}}}\]
If one of the masses is immensely large compared to the other body, as in case of planets and real objects on the planets, then the mass and size of the lighter body can be ignored. So, in case of planets, the gravitational force on surface or surface gravity is given by
\[F=\dfrac{Gm}{{{r}^{2}}}\]
So now in order to compare the gravity of planets in question, we need to find the approximate gravity of these planets.

Neptune
m= 102\[\times {{10}^{24}}kg\]
r=25000\[\times {{10}^{3}}m\]
So, the gravity on the surface would be
\[F=\dfrac{Gm}{{{r}^{2}}}\]
Plugging in the values we get
\[F\approx \] 11.0 N

Jupiter
m= 1898\[\times {{10}^{24}}kg\]
r=70000\[\times {{10}^{3}}m\]
Plugging in the values we get
\[F\approx \] 23.1 N

Earth
m= 5.97\[\times {{10}^{24}}kg\]
r=6500\[\times {{10}^{3}}m\]
Plugging in the values we get
\[F\approx \] 9.8 N

Uranus
m= 86.8\[\times {{10}^{24}}kg\]
r=25000\[\times {{10}^{3}}m\]
Plugging in the values we get
\[F\approx \] 8.7 N

Saturn
m= 868\[\times {{10}^{24}}kg\]
r=60000\[\times {{10}^{3}}m\]
Plugging in the values we get
\[F\approx \] 9.0 N

As seen from the approximate calculation above the decreasing order of gravity is Jupiter, Neptune, Saturn, Earth, Uranus.
So, Option C is correct.

So, the correct answer is “Option C”.

Note: The composition of the planets in our solar system is very different from one another. Some planets are dense and thus have greater mass even while being smaller in size while others are just clouds of gas and thus have lower mass despite having a large size. So, to compare them we need to account for size and mass both. Had the density been approximately constant we could have directly made the comparisons without having to do all the calculations manually.