Anew planet is discovered that has twice the earth's mass and twice the earth's radius. on the surface of this new planet a person who weights 500 n on earth would experience a gravitational force of
a. 125 n
b. 250 n
c. 500 n
d. 1000 n
e. 2000 n

To solve this problem we will proceed to use the expression of gravity given in Newtonian theory in terms of mass, the radius the universal gravitational constant, that is:

This expression defines as gravity on earth. On another planet with twice the mass and radius constants it would be given as,

Expressing the weight of the planet this would be then

Correct answer is B.

The weight of person on the new planet is of 250 N.  Hence, option (c) is correct.

Given data:

The weight of person on Earth is, W = 500 N.

The standard expression for the weight of person on the new planet is,

W' = mg'

Here, g' is the gravitational acceleration on the new planet.

Let us calculate the gravitational acceleration on the new planet. The standard expression for the gravitational acceleration on the new planet is,

Here,

G is the universal gravitational constant.

M is the mass of planet, which is two times the mass of Earth. (M = 2m )

R is the radius of planet, which is twice the radius of Earth. (R = 2r).

Then,

Here, g is the gravitational acceleration value on Earth. And its value on Earth is  .

Then,

.

Calculate the mass as,

So weight of person on new planet will be,

Thus, we can conclude that the weight of person on the new planet is of 250 N.

Learn more about the gravitational acceleration here:

link

an obstruction

a and b sometimes have a positive value