Question

If the radius of Earth decreased, with no change in mass, your weight would _____.

Answer 1

Answer on Question 56913, Physics, Solid State Physics

Question:

If the radius of Earth decreased with no change in mass, your weight would

a) increase

b) decrease

c) stay the same

Solution:

By the definition of the weight we have:

$$W = m g = G \frac {M _ {E} m}{R _ {E} ^ {2}},$$

here, $m$ is the mass of the person, $g = G\frac{M_E}{R_E^2}$ is the acceleration due to gravity, $G$ is the gravitational constant, $M_{E}$ is the mass of Earth, $R_{E}$ is the radius of Earth.

As we can see from the formula above, if the radius of Earth decreased with no change in mass, your weight would increase.

Answer:

a) increase