Question

If you could be transported to another planet whose Mass was the same as the Earth, but whose radius was 2 times larger than the Earth, when you stood on its surface; at a distance equal to the radius of the planet, would (a) would your mass change? (b) would your weight change? And if so, by how much would it change? Group of answer choices A) Both Mass and Weight would increase by a factor of 2B) Mass would remain the same, Weight would decrease by a factor of 4C) Mass would decrease by a factor of 4, Weight would remain the sameD) Mass would remain the same, Weight would increase by a factor of 4E) Mass would decrease by a factor of 2, Weight would remain the sameF)Both Mass and Weight would decrease by a factor of 2G) Both Mass and Weight would decrease by a factor of 4

Answer 1

Given that the mass of the planet is the same as the mass of the earth and the radius of the planet is two times that of the earth.

The mass is a fundamental property of a matter and it does not change.

The weight is the force acting on an object due to gravity.

From Newton's law of gravitation, the gravitational force is directly proportional to the product of the mass of the objects and inversely proportional to the square of the distance between them.

Thus,

`W\propto(1)/(r^2)`

Where W is the weight and r is the radius of the planet.

Thus, when the radius is doubled,

`\begin{gathered} W\propto(1)/((2r)^2) \\ \Rightarrow W\propto(1)/(4r^2) \end{gathered}`

Thus the weight will decrease by a factor of 4.

Thus, the correct answer is option B.