By what factor would your weight change if the earth's diameter were also doubled and its mass were quintupled?

Now on this question you don't need to actually use the mass and diameter of the earth as we are only looking at the factor of how much your weight would change, so you can just plug in some random numbers for the mass and radius. In my case I will use the original radius as being 2 meters and the original mass of the earth as being 20kg. You can actually just omit the mass of your body and the gravitational constant isn't necessary to be multiplied by because they will remain the same in both scenarios.

Original weight:

So the original weight in this circumstance is 5N. Now then if we double the mass to 40kg and the radius to 4m you will have the following.

So the original weight was 5N and after doubling the mass and radius the weight reduced to 2.5N. This means the factor which your weight would change by is .5 or decrease by 1/2.

Explanation:

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.