Physics

Problem

For small depths, the acceleration due to gravity decreases nearly linearly with depth. a. (i) Taking

g = 9.8\,\text{m s}^{-2}

and

R = 6.4 \times 10^{6}\,\text{m}

, calculate the values of

g

at depths

0\,\text{km}

200\,\text{km}

400\,\text{km}

and

800\,\text{km}

. b. (ii) On a set of axes with depth on the horizontal axis and

g

on the vertical axis, plot the four points obtained in (i) and draw a smooth curve through them. c. (iii) From your graph or otherwise, estimate the depth at which

g

falls to

9.0\,\text{m s}^{-2}

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