Effect of changing gravitational acceleration on weight If the local gravitational acceleration doubles (g becomes 2g), how does the weight of a given body change? Assume mass remains constant.
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Ahalf of its original weight
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Bsame as before
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Ctwice its original weight
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Dfour times its original weight
Answer
Correct Answer: twice its original weight
Explanation
Introduction / Context:Weight is the gravitational force acting on a body. This question tests the relationship between weight, mass, and gravitational acceleration, a foundational concept in mechanics.
Given Data / Assumptions:
- Mass m of the body is constant.
- Original gravitational acceleration = g; new acceleration = 2g.
- Weight W is defined as m * g.
Concept / Approach:Weight depends linearly on gravitational acceleration. Doubling g doubles the weight for the same mass.
Step-by-Step Solution:
Original weight: W_old = m * g.New weight: W_new = m * (2g) = 2 * (m * g).Hence W_new = 2 * W_old.Verification / Alternative check:Units remain force (newtons): N = kg * m/s^2. Doubling the acceleration term doubles the numerical value of the force for fixed mass.
Why Other Options Are Wrong:
- Half or same: would require g to be halved or unchanged.
- Four times: would require g to become 4g, not 2g.
Common Pitfalls:Mixing up mass (invariant in this scenario) with weight (force that changes with g). Mass is measured in kilograms; weight is measured in newtons.
Final Answer:twice its original weight