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Question 7

The variation of acceleration due to gravity $$g$$ with distance $$d$$ from the centre of the earth is best represented by ($$R$$ = Earth's radius):

1. Inside the earth ($$d < R$$):

$$g_{in} = \frac{G \cdot M_{in}}{d^2}$$

$$M_{in} = M \left( \frac{d^3}{R^3} \right)$$

$$g_{in} = \frac{G \cdot M \cdot d^3}{R^3 \cdot d^2} = \left( \frac{GM}{R^3} \right) d$$

2. Outside earth's surface ($$d >R$$)

$$g_{out} = \frac{GM}{d^2}$$

Graph:

From $$d = 0$$ to $$d = R$$, the graph must be a linearly increasing straight line.

From $$d = R$$ onwards, the graph must be a decreasing curve that asymptotically approaches the horizontal axis.

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