Physics: If you were to triple the size of the earth (r = 3r⊕) and double the mass of the earth (m = 2m⊕), how much would it change the gravity on the earth (fg = xfg⊕)?

If you were to triple the size of the earth (r = 3r⊕)

Ответ:

SmokeyRN

15.01.2022

Physics

Decreased by a factor of 4.5

Explanation:

"We have Newton formula for attraction force between 2 objects with mass and a distance between them:

$F_G = G\frac{M_1M_2}{R^2}$

where $G =6.67408 × 10^{-11} m^3/kgs^2$ is the gravitational constant on Earth. M_1, M_2 are the masses of the object and Earth itself. and R distance between, or the Earth radius.

So when R is tripled and mass is doubled, we have the following ratio of the new gravity over the old ones:

$\frac{F_G}{f_g} = \frac{G\frac{M_1M_2}{R^2}}{G\frac{M_1m_2}{r^2}}$

$\frac{F_G}{f_g} = \frac{\frac{M_2}{R^2}}{\frac{m_2}{r^2}}$

$\frac{F_G}{f_g} = \frac{M_2}{R^2}\frac{r^2}{m_2}$

$\frac{F_G}{f_g} = \frac{M_2}{m_2}(\frac{r}{R})^2$

Since M_2 = 2m_2 and r = R/3

$\frac{F_G}{f_g} = \frac{2}{3^2} = 2/9 = 1/4.5$

So gravity would have been decreased by a factor of 4.5

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Ответ:

lilisncz

06.09.2020

Physics

Explanation:

11.) d

12.) f

13.) c

15.) i

pls give me brainliest

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If you were to triple the size of the earth (r = 3r⊕) and double the mass of the earth (m = 2m⊕), how much would it change the gravity on the earth (fg = xfg⊕)?

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