Question

Where would the weight of an explorer be greater?The summit of Chimborazo, in Ecuador, which is at a distance of about 6,384 km6,384 km from the Earth’s center.The bottom of the Mariana Trench, in the western Pacific ocean, which is nearly 6,370 km6,370 km from the center of the Earth.On the surface of Earth on the Equator line.

Answer 1

Answer:

The weight would be greater in the Mariana because the radius of the earth is lower.

Explanation:

We will make a comparison through constants and equations to see which one is more viable.

Using the force of gravity

$F = \frac{Gm}{R^2}$

F = Gravity force

G= Gravitational constant

m= mass

R is the radius of the earth, $R_E = 6384$ km and $R_M =6370$  km

Density $(\rho)$ is equal in both places,

-Gravity Force at Ecuador, $F_E=\frac{Gm}{R_E^2}$

-Gravity Force at bottom of Mariana trench, $F_M=\frac{Gm}{R_M^2}$

Making the relation,

$\frac{F_E}{F_M}= \frac{\frac{Gm}{R_E^2}}{\frac{Gm}{R_M^2}}$

$\frac{F_E}{F_M}= (\frac{R_M}{R_E})^2$

For the Ecuador,

$F_E= F_M * \frac{R_M^2}{R_E^2}$

If we take $F_M * R_M^2$ as a constant X then

$F_E= \frac{X}{R_E^2}$

So the gravity force of the place is inversely proportion of the radius

Same for the Mariana trench,

$FM= \frac{X}{R_M^2}$

Then, the weight would be greater in the Mariana because the radius of the earth is lower.