Question

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

Answer 1

weight will be become
`(W)/(4)`

So option (C) will be correct answer

Step-by-step explanation:

We have given mass of the earth is
`M_E` and radius of earth is
`R_E`

Acceleration due to gravity on earth is given by
`g=(GM_E)/(R_E^2)`

Weight is equal to
`W=mg`, as mass is always conserved so weight is dependent on acceleration due to gravity

Now radius is
`2R_E`

So acceleration due to gravity is
`g_(new)=(GM_E)/((2R_E)^2)=(GM_E)/(4R_E^2)=(g)/(4)`

As weight is directly related to acceleration due to gravity

So weight will be become
`(W)/(4)`

So option (C) will be correct answer