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Roman Purgstaller · Answer 1 · 2023-09-19T09:25:14+0000

$F=11.375\text{ Newtons}$

Step-by-step explanation

the acceleration due to gravity formula is given by:

$\begin{gathered} g=(GM)/(R^2)^{} \\ \text{where} \\ G\text{ is the universal gravitational constatn G=6.674 }\cdot10^(-11)\frac{m^3}{\operatorname{kg}\cdot s^2} \\ R\text{ is the radius of the massive body ( in meters)} \\ g\text{ is the acceleration due to gravity} \\ M\text{ is the mass of the massive body ( kg)} \end{gathered}$

Step 1

Find g(acceleration due to gravity)

Let

$\begin{gathered} M=\text{ mass of the moon=7.35}\cdot10^(22)\operatorname{kg} \\ G=\text{=6.674 }\cdot10^(-11)\frac{m^3}{\operatorname{kg}\cdot s^2} \\ R=\text{radius of the moon=}1.74\cdot10^6m \end{gathered}$

now, replace in the formula

$\begin{gathered} g=(GM)/(R^2)^{} \\ g=\frac{\text{6.674 }\cdot10^(-11)\frac{m^3}{\operatorname{kg}\cdot s^2}\cdot\text{7.35}\cdot10^(22)\operatorname{kg}}{(1.74\cdot10^6m)^2} \\ g=(4.90539\cdot10^(12))/((3.0276\cdot10^(12))) \\ g=1.62(m)/(s^2) \end{gathered}$

Step 2

to find the force , use the formula

$\begin{gathered} F=\text{mg} \\ \text{where m is the mass of the object} \\ g\text{ is the acceleration due to gravity} \end{gathered}$

replace

$\begin{gathered} F=7\operatorname{kg}\cdot1.625\text{ }(m)/(s^2) \\ F=11.375\text{ Newtons} \end{gathered}$

therefore, the force would be

11.375 N

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