Question

An astronaut weighs 700 N on Earth. What is
the best approximation of his new weight on
a planet with a radius that is two times that
of Earth, and a mass three times that of
Earth?
A. 200 N
B. 500 N
C. 700 N
D. 900 N
E. 1200 N​

Answer 1

Answer:

b. 500 N

pls see attachment for detailed explanation

Answer 2

Answer:

500 N

Explanation:

M = Mass of the Earth

r = Radius of Earth

G = Gravitational constant

Acceleration due to gravity on Earth

$g_e=G\frac{M}{r^2}$

Acceleration due to gravity on the other planet

$g=G\frac{3M}{(2r)^2}\\\Rightarrow g=G\frac{3M}{(4r^2}$

Dividing the Equations we get

$\frac{g_e}{g}=\frac{G\frac{M}{r^2}}{G\frac{3M}{(4r^2}}\\\Rightarrow \frac{g_e}{g}=\frac{4}{3}\\\Rightarrow g=\frac{3}{4}g_e$

Multiplying with mass on both sides

$mg=mg_e\frac{3}{4}\\\Rightarrow mg=700\times \frac{3}{4}\\\Rightarrow F=525\ N$

Weight of astronaut on the other planet is 525 N