At the surface of Jupiter's moon lo, the acceleration due to gravity is g=1.8

Result:
(a)$4.49\text{kg}$
(b)$8.13\text{N}$
Solution:
(a) To find the watermelon's mass on Earth's surface, we can use the formula relating weight, mass, and acceleration due to gravity:
$\text{Weight}=\text{mass}\times \text{acceleration due to gravity}\text{(1)}$
Given that the weight of the watermelon on Earth's surface is $44.0\text{N}$ and the acceleration due to gravity on Earth is approximately $9.81{\text{m/s}}^2$, we can rearrange equation (1) to solve for the mass:
$\text{mass}=\frac{\text{weight}}{\text{acceleration due to gravity}}$
Substituting the given values into the equation, we get:
${\text{mass}}_{\text{Earth}}=\frac{44.0\text{N}}{9.81{\text{m/s}}^2}=4.49\text{kg}$
Therefore, the watermelon's mass on Earth's surface is $4.49\text{kg}$.
(b) To determine the mass and weight of the watermelon on the surface of Jupiter's moon Io, we can use the same formula (equation (1)) and substitute the given values. The acceleration due to gravity on Io is stated as $g=1.81{\text{m/s}}^2$.
Using equation (1), we have:
${\text{Weight}}_{\text{Io}}={\text{mass}}_{\text{Io}}\times g_{\text{Io}}$
We want to find the mass on Io, so we rearrange the equation:
${\text{mass}}_{\text{Io}}=\frac{{\text{Weight}}_{\text{Io}}}{g_{\text{Io}}}$
Since weight is equal to mass multiplied by the acceleration due to gravity, the weight on Io can be calculated as:
${\text{Weight}}_{\text{Io}}={\text{mass}}_{\text{Io}}\times g_{\text{Earth}}$
Substituting this into the previous equation, we have:
${\text{mass}}_{\text{Io}}=\frac{{\text{mass}}_{\text{Io}}\times g_{\text{Earth}}}{g_{\text{Io}}}$
Simplifying the equation, we find:
${\text{mass}}_{\text{Io}}(1-\frac{g_{\text{Earth}}}{g_{\text{Io}}})=0$
Since the mass cannot be zero, we conclude that the mass of the watermelon on the surface of Io is indeterminate. This means that we cannot calculate the mass accurately without additional information.
However, we can calculate the weight of the watermelon on Io using the equation:
${\text{Weight}}_{\text{Io}}={\text{mass}}_{\text{Earth}}\times g_{\text{Io}}$
Substituting the known values, we have:
${\text{Weight}}_{\text{Io}}=4.49\text{kg}\times 1.81{\text{m/s}}^2=8.13\text{N}$
Therefore, the watermelon would weigh approximately $8.13\text{N}$ on the surface of Jupiter's moon Io.

(a) The weight of an object on Earth's surface is given by the equation:
$W=mg$
where $W$ is the weight, $m$ is the mass, and $g$ is the acceleration due to gravity. Rearranging the equation, we can solve for mass:
$m=\frac{W}{g}$
Substituting the given values, we have:
$m=\frac{44.0\text{N}}{9.81\frac{m}{s^2}}$
Simplifying, we find that the mass of the watermelon on Earth's surface is:
$m=4.49\text{kg}$
(b) To find the mass and weight of the watermelon on the surface of lo, we can use the same equation, but with the acceleration due to gravity on lo, denoted as $g_{lo}$. Let's denote the mass on lo as $m_{lo}$ and the weight on lo as $W_{lo}$. Therefore:
$W_{lo}=m_{lo}·g_{lo}$
We are given that $g_{lo}=1.81\frac{m}{s^2}$. To find the mass on lo, we can rearrange the equation:
$m_{lo}=\frac{W_{lo}}{g_{lo}}$
Since the mass is the same regardless of the location, we can substitute the value we found for the mass on Earth's surface ($m=4.49\text{kg}$) into the equation:
$m_{lo}=\frac{4.49\text{kg}}{1.81\frac{m}{s^2}}$
Simplifying, we find that the mass of the watermelon on the surface of lo is:
$m_{lo}=2.48\text{kg}$
To find the weight on the surface of lo, we can substitute the values of mass and gravity on lo into the equation:
$W_{lo}=m_{lo}·g_{lo}$
$W_{lo}=2.48\text{kg}·1.81\frac{m}{s^2}$
Simplifying, we find that the weight of the watermelon on the surface of lo is:
$W_{lo}=4.49\text{N}$