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A 5 kg object is on the ground, then at heights of 1R, 2R, 3R and 4R above the ground, where R is…

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A $5\ \text{kg}$ object is on the ground, then at heights of $1R$ , $2R$ , $3R$ and $4R$ above the ground, where $R$ is the Earth's radius. Find the Earth's pull at each place. What pattern do you see?

Need a reminder? The key ideaShow

Near a planet, $g = \dfrac{GM}{R^2}$ ; at a distance $r$ from its centre, $g$ falls as $\dfrac{1}{r^2}$ . On the Earth's surface $g = 9.8\ \text{m/s}^2$ ; at $n$ Earth radii above the ground it is $\dfrac{9.8}{(1 + n)^2}\ \text{m/s}^2$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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