Final answer:
On a planet with twice the mass and twice the radius of Earth, you would weigh half your Earth weight. Therefore, if you weigh 150 lb on Earth, on this new planet you would weigh 75 lb.
Step-by-step explanation:
If you weigh 150 lb on Earth and you stood on a planet with twice the mass of Earth and a radius twice as large as Earth's, your weight would be affected by the gravitational pull of that planet. The gravitational force that an object experiences is directly proportional to the mass of the planet and inversely proportional to the square of the radius of the planet, according to the formula F = G(m1*m2/r²), where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between the centers of the two masses.
Since the mass is doubled and the radius is doubled, the new gravitational acceleration at the surface of this planet would be (2 * mass of Earth) / (2 * radius of Earth)² = 1/2 the Earth's gravitational acceleration. Hence, on this new planet, you would weigh half of your Earth weight. Thus, the answer is 75 lb.