Weight variation with location: If g1 and g2 are the local gravitational accelerations at two mountain locations A and B respectively, by what factor will the weight of a body change when transported from A to B (assume mass remains constant)?

Introduction / Context:

In engineering mechanics and physics, the weight of a body is the gravitational force acting on its mass. Although the mass of a body is invariant with location, its weight can change slightly from place to place because the local acceleration due to gravity varies with altitude, latitude, and underlying geology.

Given Data / Assumptions:

• Two locations: mountain A with gravitational acceleration g1 and mountain B with gravitational acceleration g2.
• The same body (constant mass m) is moved from A to B.
• Air buoyancy and other minor effects are neglected.

Concept / Approach:

Weight W is defined as W = m * g. For the same mass m at different locations with acceleration g, weight scales directly with g. Therefore, the ratio of the new weight to the old weight equals the ratio of the corresponding gravitational accelerations.

Step-by-Step Solution:

Verification / Alternative check:

If g2 = g1 there is no change and g2 / g1 = 1, which is consistent. If g2 is smaller (higher altitude), the factor is less than 1, indicating reduced weight—again consistent with experience.

Why Other Options Are Wrong:

• g1 / g2 reverses the change direction.
• (g1 + g2) / 2 is an average, not a scaling factor for weight change.
• (g2 - g1) / g1 gives a fractional change, not the required multiplier.
• 'Independent of location' contradicts the definition W = m * g.

Common Pitfalls:

• Confusing mass (constant) with weight (varies with g).

Final Answer:

g2 / g1