If Earth's mass decreased to one half its original mass, with no change in radius, then your weight would _____.

Question

BlackTom AI · Accepted Answer

Gravitational force near Earth’s surface is F = G M m / R^2, so weight depends linearly on Earth's mass M and inversely on the square of its radius R.

1) Relevant knowledge points and concepts
- Weight is the gravitational force W on a person of mass m due to Earth: W = G M m / R^2.
- G is the gravitational constant, M is Earth’s mass, R is Earth’s radius. If R is unchanged, weight scales directly with M.
- Distinguish mass (m, intrinsic) from weight (force due to gravity).

2) Complete reasoning step by step
- Let the original Earth mass be M and your original weight be W0 = G M m / R^2.
- If Earth’s mass decreases to one half: M' = (1/2) M, while R stays the same.

3) Calculations with intermediate steps
- New weight W' = G M' m / R^2 = G (1/2 M) m / R^2
- Factor out 1/2: W' = (1/2) [G M m / R^2] = (1/2) W0

4) Why the correct answer is correct
- Because weight is directly proportional to Earth’s mass when radius is constant, halving M halves the gravitational force; thus your weight becomes one half of its original value.

5) Why the other choices are incorrect
- (a) stay the same: incorrect because changing M changes g and therefore weight. Keeping R constant does not prevent weight from changing if M changes.
- (c) decrease to one quarter your original weight: incorrect because a quartering of weight would require Earth's mass to fall to one quarter (or radius to change so R^2 increases by 4); neither is given.
- (d) none of the above: incorrect because option (b) correctly describes the change.

6) Conclusion
- The final weight is one half the original weight, so the correct choice is b. decrease to one half your original weight.

If Earth's mass decreased to one half its original mass, with no change in radius, then your weight would _____.单项选择题

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