Assume the earth to be a nonrotating sphere with mass ME and radius RE. If an astronaut weights W on the ground, what is his weight when he is 2RE above the surface of the earth?

a) W/2

b) W/9

c) W/4

d) W/3

Question

contestada

Respuesta :

aristeus aristeus · Answer 1 · 2020-01-14T07:33:01+01:00

Answer:

weight will be become [tex]\frac{W}{4}[/tex]

So option (C) will be correct answer

Explanation:

We have given mass of the earth is [tex]M_E[/tex] and radius of earth is [tex]R_E[/tex]

Acceleration due to gravity on earth is given by [tex]g=\frac{GM_E}{R_E^2}[/tex]

Weight is equal to [tex]W=mg[/tex], as mass is always conserved so weight is dependent on acceleration due to gravity

Now radius is [tex]2R_E[/tex]

So acceleration due to gravity is [tex]g_{new}=\frac{GM_E}{(2R_E)^2}=\frac{GM_E}{4R_E^2}=\frac{g}{4}[/tex]

As weight is directly related to acceleration due to gravity

So weight will be become [tex]\frac{W}{4}[/tex]

So option (C) will be correct answer