# Which of the sketched graphs below illustrates the correct variation of…

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A. A

B. B

C. C

D. D

B

## DETAILS…

The sketched graph in option B illustrates the correct variation of the gravitational force Fg between two objects and the distance, d, between the centers.

Recall that the correct formula for calculating Fg will be Newton’s law of universal gravitation which states thus:

Fg = Gm₁m₂/d²

If G, m₁, and m₂ are constants, then it follows that:

Fg = k/d²

This implies that

• Fg is inversely proportional to d².
• Since d has a power of 2, the graph will never be a straight line but a curve.
• As Fg increases, it is expected that d decreases.
• When Fg is zero, d will be infinite, and when d is zero, Fg will approach infinity.

The graph shown in option B is the closest and most suitable to explain this relation.

### Now for the right answer to the above question:

1. Option A is incorrect. the graph will never start at origin because both parameters are inversely related.
2. Option B is correct. yes, the graph is expected to be a curve because the power of d is 2.
3. C is not correct. this is wrong because Fg must change as d changes.
4. D is not the correct answer. this is very wrong because the graph is not expected to start from the origin.

## KEY-POINTS…

• Fg is inversely proportional to d².
• This implies that one increases when the other decreases.
• This also implies that they will never start at the origin.
• This also implies that the graph will be a curve.
• If one of the parameters of any formula has a power greater than one, then the graph must be a curve.

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/ culled from 2021 JAMB-UTME PHYSICS question 10 BATCH-B /

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