Chapter 7, Problem 85A

To determine

The value of g on the surface of Jupiter.

Answer to Problem 85A

  $29.4{\text{m/s}}^{\text{2}}$

Explanation of Solution

Given:

Jupiter’s mass is about $300$ times the mass of Earth.

Jupiter’s radius is about $10$ times the radius of Earth.

Formula used:

The value of g on any planet can be obtained by:

  $g=\frac{GM}{R^2}$

Where, $G$ is the gravitational constant, $R$ is the radius of the planet, and $M$ is the mass of the planet.

Calculation:

The value of gravitational constant is,=

  $G=6.67\times {10}^{-11}\text{N}{\text{.m}}^{\text{2}}{\text{/kg}}^{\text{2}}$

The value of g on the Earth’s surface is,

  $g=9.8{\text{m/s}}^{\text{2}}$

Then, using the formula of gravitational field, it can be written as

  $\begin{array}{c}{g}_{Earth}=\frac{G{M}_{Earth}}{R_{Earth}^2}\\ 9.8=\frac{G{M}_{Earth}}{R_{Earth}^2}\end{array}$

And, the value of $g$ on Jupiter’s surface is,

  $\begin{array}{c}{g}_{Jupiter}=\frac{G{M}_{Jupiter}}{R_{Jupiter}^2}\\ =\frac{G\left(300M_{Earth}\right)}{{\left(10R_{Earth}\right)}^2}\\ =3g_{Earth}\\ =3\times 9.8\\ =29.4{\text{m/s}}^{\text{2}}\end{array}$

Conclusion:

Thus, the value of g on the Jupiter is $29.4{\text{m/s}}^{\text{2}}$ .