Question

How would your present weight change if Earth had twice the mass that it does now?

Answer 1

Twice the mass means twice the acceleration due to gravity which will increase acceleration by the factor of 2 thus the weight will be double the time.

Answer 2

The weight would be doubled

Step-by-step explanation:

The weight of an object on Earth is equal to the gravitational attraction exerted by the Earth on the object:

`F=G(m M)/(r^2)`

where

G is the gravitational constant

m is the mass of the object

M is the mass of the Earth

r is the distance between the object and the Earth's center

We see that the weight (F) is directly proportional to the Earth's mass (M): so, if the Earth had twice the mass that it does now (M'=2M), then the weight F would be also doubled, in fact:

`F'=G(mM')/(r^2)=G(m(2M))/(r^2)=2G(mM)/(r^2)=2F`