Question

What will an object weigh on the Moon's surface if it weighs 100 N on Earth's surface? (b) How many Earth radii must this same object be from the center of Earth if it is to weigh the same as it does on the Moon?

Answer 1

Part a)

W = 16.7 N

Part b)

r = 2.45 R

Step-by-step explanation:

Part a)

As we know that acceleration due to gravity on the surface of moon is 1/6 times the gravity on the surface of earth

So the force due to gravity will decrease by the factor of 6

so we will have

`W_(moon) = (1)/(6)W_(earth)`

`W_(moon) = (1)/(6)(100)`

`W_(moon) = 16.7 N`

Part b)

For the same value of the weight as the surface of moon the acceleration due to gravity of earth must be 1/6 times

so we have

`(GM)/(r^2) = (GM)/(6R^2)`

`r^2 = 6R^2`

`r = 2.45 R`